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Theorem coeq1i 4972
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 4970 . 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 1649    o. ccom 4822
This theorem is referenced by:  coeq12i  4976  cocnvcnv1  5320  hashgval  11548  imasdsval2  13669  prds1  15647  upxp  17576  uptx  17578  pf1mpf  19839  hoico2  23108  hoid1ri  23141  nmopcoadj2i  23453  pjclem3  23548  erdsze2lem2  24669  pprodcnveq  25447  diblss  31285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-in 3270  df-ss 3277  df-br 4154  df-opab 4208  df-co 4827
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