Theorem ineq2i 3379

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 3376	. 2 |- ( A = B -> ( C i^i A ) = ( C i^i B ) )
3	1, 2	ax-mp 5	1 |- ( C i^i A ) = ( C i^i B )

Syntax hints:   = wceq 1373   i^i cin 3173

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-in 3180

This theorem is referenced by:  in4  3397  inindir  3399  indif2  3425  difun1  3441  dfrab3ss  3459  dfif3  3593  intunsn  3937  rint0  3938  riin0  4013  res0  4982  resres  4990  resundi  4991  resindi  4993  inres  4995  resiun2  4998  resopab  5022  dfse2  5074  dminxp  5146  imainrect  5147  resdmres  5193  funimacnv  5369  unfiin  7049  sbthlemi5  7089  dmaddpi  7473  dmmulpi  7474  fsumiun  11903  ressval2  13013  ressval3d  13019  lgsquadlem3  15671