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Theorem coeq2i 4637
Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000.)
Hypothesis
Ref Expression
coeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
coeq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem coeq2i
StepHypRef Expression
1 coeq1i.1 . 2 𝐴 = 𝐵
2 coeq2 4635 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 7 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1299  ccom 4481
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-in 3027  df-ss 3034  df-br 3876  df-opab 3930  df-co 4486
This theorem is referenced by:  coeq12i  4640  cocnvcnv2  4986  co01  4989  cocnvres  4999  fcoi1  5239  dftpos2  6088  tposco  6102
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