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Metamath Proof Explorer

Theorem coeq12i

Description: Equality inference for composition of two classes. (Contributed by FL, 7-Jun-2012)

Ref Expression
Hypotheses coeq12i.1 ⊢ 𝐴 = 𝐵
coeq12i.2 ⊢ 𝐶 = 𝐷
Assertion coeq12i ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐷 )

Proof

Step Hyp Ref Expression
1 coeq12i.1 ⊢ 𝐴 = 𝐵
2 coeq12i.2 ⊢ 𝐶 = 𝐷
3 1 coeq1i ⊢ ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 )
4 2 coeq2i ⊢ ( 𝐵 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐷 )
5 3 4 eqtri ⊢ ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐷 )