Theorem ineq2i 3305

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 3302	. 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 1335   i^i cin 3101

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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108

This theorem is referenced by:  in4  3323  inindir  3325  indif2  3351  difun1  3367  dfrab3ss  3385  dfif3  3518  intunsn  3845  rint0  3846  riin0  3920  res0  4870  resres  4878  resundi  4879  resindi  4881  inres  4883  resiun2  4886  resopab  4910  dfse2  4959  dminxp  5030  imainrect  5031  resdmres  5077  funimacnv  5246  unfiin  6870  sbthlemi5  6905  dmaddpi  7245  dmmulpi  7246  fsumiun  11374