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Theorem coeq1i 4705
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 4703 . 2  |-  ( A  =  B  ->  ( A  o.  C )  =  ( B  o.  C ) )
31, 2ax-mp 5 1  |-  ( A  o.  C )  =  ( B  o.  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1332    o. ccom 4550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-in 3081  df-ss 3088  df-br 3937  df-opab 3997  df-co 4555
This theorem is referenced by:  coeq12i  4709  cocnvcnv1  5056  upxp  12478  uptx  12480
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