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Theorem coeq2i 4627
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  |-  ( C  o.  A )  =  ( C  o.  B
)

Proof of Theorem coeq2i
StepHypRef Expression
1 coeq1i.1 . 2  |-  A  =  B
2 coeq2 4625 . 2  |-  ( A  =  B  ->  ( C  o.  A )  =  ( C  o.  B ) )
31, 2ax-mp 7 1  |-  ( C  o.  A )  =  ( C  o.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1296    o. ccom 4471
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 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-in 3019  df-ss 3026  df-br 3868  df-opab 3922  df-co 4476
This theorem is referenced by:  coeq12i  4630  cocnvcnv2  4976  co01  4979  cocnvres  4989  fcoi1  5226  dftpos2  6064  tposco  6078
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