let Al be QC-alphabet ; :: thesis: for p being Element of CQC-WFF Al

for A being non empty set

for J being interpretation of Al,A

for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let p be Element of CQC-WFF Al; :: thesis: for A being non empty set

for J being interpretation of Al,A

for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let A be non empty set ; :: thesis: for J being interpretation of Al,A

for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let J be interpretation of Al,A; :: thesis: for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let v be Element of Valuations_in (Al,A); :: thesis: for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let Sub be CQC_Substitution of Al; :: thesis: ( J,v |= [p,Sub] iff J,v |= p )

( J,v |= [p,Sub] iff J,v |= [p,Sub] `1 ) by SUBLEMMA:def 2;

hence ( J,v |= [p,Sub] iff J,v |= p ) ; :: thesis: verum

for A being non empty set

for J being interpretation of Al,A

for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let p be Element of CQC-WFF Al; :: thesis: for A being non empty set

for J being interpretation of Al,A

for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let A be non empty set ; :: thesis: for J being interpretation of Al,A

for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let J be interpretation of Al,A; :: thesis: for v being Element of Valuations_in (Al,A)

for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let v be Element of Valuations_in (Al,A); :: thesis: for Sub being CQC_Substitution of Al holds

( J,v |= [p,Sub] iff J,v |= p )

let Sub be CQC_Substitution of Al; :: thesis: ( J,v |= [p,Sub] iff J,v |= p )

( J,v |= [p,Sub] iff J,v |= [p,Sub] `1 ) by SUBLEMMA:def 2;

hence ( J,v |= [p,Sub] iff J,v |= p ) ; :: thesis: verum