let f1, f2 be Element of InnAut G; :: thesis: ( ( for a being Element of G holds f1 . a = a |^ b ) & ( for a being Element of G holds f2 . a = a |^ b ) implies f1 = f2 )

assume that

A2: for a being Element of G holds f1 . a = a |^ b and

A3: for a being Element of G holds f2 . a = a |^ b ; :: thesis: f1 = f2

for a being Element of G holds f1 . a = f2 . a

assume that

A2: for a being Element of G holds f1 . a = a |^ b and

A3: for a being Element of G holds f2 . a = a |^ b ; :: thesis: f1 = f2

for a being Element of G holds f1 . a = f2 . a

proof

hence
f1 = f2
; :: thesis: verum
let a be Element of G; :: thesis: f1 . a = f2 . a

thus f1 . a = a |^ b by A2

.= f2 . a by A3 ; :: thesis: verum

end;thus f1 . a = a |^ b by A2

.= f2 . a by A3 ; :: thesis: verum