Metamath Proof Explorer


Theorem feq123

Description: Equality theorem for functions. (Contributed by FL, 16-Nov-2008)

Ref Expression
Assertion feq123 F = G A = C B = D F : A B G : C D

Proof

Step Hyp Ref Expression
1 simp1 F = G A = C B = D F = G
2 simp2 F = G A = C B = D A = C
3 simp3 F = G A = C B = D B = D
4 1 2 3 feq123d F = G A = C B = D F : A B G : C D