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Theorem coeq12i 4774
Description: Equality inference for composition of two classes. (Contributed by FL, 7-Jun-2012.)
Hypotheses
Ref Expression
coeq12i.1 𝐴 = 𝐵
coeq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
coeq12i (𝐴𝐶) = (𝐵𝐷)

Proof of Theorem coeq12i
StepHypRef Expression
1 coeq12i.1 . . 3 𝐴 = 𝐵
21coeq1i 4770 . 2 (𝐴𝐶) = (𝐵𝐶)
3 coeq12i.2 . . 3 𝐶 = 𝐷
43coeq2i 4771 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2191 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff set class
Syntax hints:   = wceq 1348  ccom 4615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-in 3127  df-ss 3134  df-br 3990  df-opab 4051  df-co 4620
This theorem is referenced by: (None)
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