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Theorem coeq2i 5036
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 5034 . 2  |-  ( A  =  B  ->  ( C  o.  A )  =  ( C  o.  B ) )
31, 2ax-mp 5 1  |-  ( C  o.  A )  =  ( C  o.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653    o. ccom 4885
This theorem is referenced by:  coeq12i  5039  cocnvcnv2  5384  co01  5387  fcoi1  5620  dftpos2  6499  tposco  6513  canthp1  8534  cats1co  11825  imasdsf1olem  18408  evlsval  19945  evl1var  19957  pf1ind  19980  hoico1  23264  hoid1i  23297  pjclem1  23703  pjclem3  23705  pjci  23708  dfpo2  25383  mvdco  27379  cdlemk45  31818
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-in 3329  df-ss 3336  df-br 4216  df-opab 4270  df-co 4890
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