Theorem ineq2i 3402

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 3399	. 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 1395   i^i cin 3196

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-in 3203

This theorem is referenced by:  in4  3420  inindir  3422  indif2  3448  difun1  3464  dfrab3ss  3482  dfif3  3616  intunsn  3961  rint0  3962  riin0  4037  res0  5009  resres  5017  resundi  5018  resindi  5020  inres  5022  resiun2  5025  resopab  5049  dfse2  5101  dminxp  5173  imainrect  5174  resdmres  5220  funimacnv  5397  unfiin  7088  sbthlemi5  7128  dmaddpi  7512  dmmulpi  7513  fsumiun  11988  ressval2  13099  ressval3d  13105  lgsquadlem3  15758