Theorem ineq2i 3362

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 3359	. 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 1364   i^i cin 3156

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-in 3163

This theorem is referenced by:  in4  3380  inindir  3382  indif2  3408  difun1  3424  dfrab3ss  3442  dfif3  3575  intunsn  3913  rint0  3914  riin0  3989  res0  4951  resres  4959  resundi  4960  resindi  4962  inres  4964  resiun2  4967  resopab  4991  dfse2  5043  dminxp  5115  imainrect  5116  resdmres  5162  funimacnv  5335  unfiin  6996  sbthlemi5  7036  dmaddpi  7409  dmmulpi  7410  fsumiun  11659  ressval2  12769  ressval3d  12775  lgsquadlem3  15404