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Theorem coeq2i 4844
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 4842 . 2  |-  ( A  =  B  ->  ( C  o.  A )  =  ( C  o.  B ) )
31, 2ax-mp 8 1  |-  ( C  o.  A )  =  ( C  o.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    o. ccom 4693
This theorem is referenced by:  coeq12i  4847  cocnvcnv2  5184  co01  5187  fcoi1  5415  dftpos2  6251  tposco  6265  canthp1  8276  cats1co  11506  imasdsf1olem  17937  evlsval  19403  evl1var  19415  pf1ind  19438  hoico1  22336  hoid1i  22369  pjclem1  22775  pjclem3  22777  pjci  22780  dfpo2  24112  crimmt1  25146  mvdco  27388  cdlemk45  31136
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-in 3159  df-ss 3166  df-br 4024  df-opab 4078  df-co 4698
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