Theorem ineq2i 3421

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 3418	. 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 1398   i^i cin 3212

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-in 3219

This theorem is referenced by:  in4  3439  inindir  3441  indif2  3467  difun1  3483  dfrab3ss  3501  dfif3  3638  intunsn  3989  rint0  3990  riin0  4065  res0  5044  resres  5052  resundi  5053  resindi  5055  inres  5057  resiun2  5060  resopab  5084  dfse2  5137  dminxp  5209  imainrect  5210  resdmres  5256  funimacnv  5434  unfiin  7188  sbthlemi5  7233  dmaddpi  7642  dmmulpi  7643  hashtpgim  11221  fsumiun  12167  ressval2  13296  ressval3d  13302  lgsquadlem3  15969