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Theorem coeq1i 4859
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 4857 . 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 1632    o. ccom 4709
This theorem is referenced by:  coeq12i  4863  cocnvcnv1  5199  hashgval  11356  imasdsval2  13435  prds1  15413  upxp  17333  uptx  17335  pf1mpf  19451  hoico2  22353  hoid1ri  22386  nmopcoadj2i  22698  pjclem3  22793  erdsze2lem2  23750  pprodcnveq  24494  crimmt2  25250  diblss  31982
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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