Theorem ineq2i 3279

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 3276	. 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 1332   i^i cin 3075

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082

This theorem is referenced by:  in4  3297  inindir  3299  indif2  3325  difun1  3341  dfrab3ss  3359  dfif3  3492  intunsn  3817  rint0  3818  riin0  3892  res0  4831  resres  4839  resundi  4840  resindi  4842  inres  4844  resiun2  4847  resopab  4871  dfse2  4920  dminxp  4991  imainrect  4992  resdmres  5038  funimacnv  5207  unfiin  6822  sbthlemi5  6857  dmaddpi  7157  dmmulpi  7158  fsumiun  11278