Metamath Proof Explorer


Theorem imaeq12d

Description: Equality theorem for image. (Contributed by Mario Carneiro, 4-Dec-2016)

Ref Expression
Hypotheses imaeq1d.1 φ A = B
imaeq12d.2 φ C = D
Assertion imaeq12d φ A C = B D

Proof

Step Hyp Ref Expression
1 imaeq1d.1 φ A = B
2 imaeq12d.2 φ C = D
3 1 imaeq1d φ A C = B C
4 2 imaeq2d φ B C = B D
5 3 4 eqtrd φ A C = B D