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Theorem coeq2i 4860
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 4858 . 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 1632    o. ccom 4709
This theorem is referenced by:  coeq12i  4863  cocnvcnv2  5200  co01  5203  fcoi1  5431  dftpos2  6267  tposco  6281  canthp1  8292  cats1co  11522  imasdsf1olem  17953  evlsval  19419  evl1var  19431  pf1ind  19454  hoico1  22352  hoid1i  22385  pjclem1  22791  pjclem3  22793  pjci  22796  dfpo2  24183  crimmt1  25249  mvdco  27491  cdlemk45  31758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-in 3172  df-ss 3179  df-br 4040  df-opab 4094  df-co 4714
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