Theorem coeq1i 4698

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

Step	Hyp	Ref	Expression
1		coeq1i.1	. 2 |- A = B
2		coeq1 4696	. 2 |- ( A = B -> ( A o. C ) = ( B o. C ) )
3	1, 2	ax-mp 5	1 |- ( A o. C ) = ( B o. C )

Syntax hints:   = wceq 1331   o. ccom 4543

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-in 3077  df-ss 3084  df-br 3930  df-opab 3990  df-co 4548

This theorem is referenced by:  coeq12i  4702  cocnvcnv1  5049  upxp  12441  uptx  12443