Theorem coeq1i 4934

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 4932	. 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 1402   o. ccom 4773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-in 3226  df-ss 3233  df-br 4126  df-opab 4188  df-co 4778

This theorem is referenced by:  coeq12i  4938  cocnvcnv1  5293  upxp  15296  uptx  15298