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Theorem coeq1i 4843
Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000.)
Hypothesis
Ref Expression
coeq1i.1  |-  A  =  B
Assertion
Ref Expression
coeq1i  |-  ( A  o.  C )  =  ( B  o.  C
)

Proof of Theorem coeq1i
StepHypRef Expression
1 coeq1i.1 . 2  |-  A  =  B
2 coeq1 4841 . 2  |-  ( A  =  B  ->  ( A  o.  C )  =  ( B  o.  C ) )
31, 2ax-mp 8 1  |-  ( A  o.  C )  =  ( B  o.  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    o. ccom 4693
This theorem is referenced by:  coeq12i  4847  cocnvcnv1  5183  hashgval  11340  imasdsval2  13419  prds1  15397  upxp  17317  uptx  17319  pf1mpf  19435  hoico2  22337  hoid1ri  22370  nmopcoadj2i  22682  pjclem3  22777  erdsze2lem2  23735  pprodcnveq  24423  crimmt2  25147  diblss  31360
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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