Theorem ineq2i 3164

Description: Equality inference for intersection of two classes. (Contributed by NM, 26-Dec-1993.)

Hypothesis

Ref	Expression
ineq1i.1	|- A = B

Assertion

Ref	Expression
ineq2i	|- ( C i^i A ) = ( C i^i B )

Proof of Theorem ineq2i

Step	Hyp	Ref	Expression
1		ineq1i.1	. 2 |- A = B
2		ineq2 3161	. 2 |- ( A = B -> ( C i^i A ) = ( C i^i B ) )
3	1, 2	ax-mp 7	1 |- ( C i^i A ) = ( C i^i B )

Syntax hints:   = wceq 1284   i^i cin 2972

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-in 2979

This theorem is referenced by:  in4  3182  inindir  3184  indif2  3208  difun1  3224  dfrab3ss  3242  dfif3  3364  intunsn  3674  rint0  3675  riin0  3749  res0  4634  resres  4642  resundi  4643  resindi  4645  inres  4647  resiun2  4649  resopab  4672  dfse2  4718  dminxp  4785  imainrect  4786  resdmres  4832  funimacnv  4995  dmaddpi  6515  dmmulpi  6516