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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