Theorem ineq2i 3135

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 3132	. 2 |- ( A = B -> ( C i^i A ) = ( C i^i B ) )
3	1, 2	ax-mp 7	1 |- ( C i^i A ) = ( C i^i B )

Syntax hints:   = wceq 1243   i^i cin 2916

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924

This theorem is referenced by:  in4  3153  inindir  3155  indif2  3181  difun1  3197  dfrab3ss  3215  dfif3  3343  intunsn  3653  rint0  3654  riin0  3728  res0  4616  resres  4624  resundi  4625  resindi  4627  inres  4629  resiun2  4631  resopab  4652  dfse2  4698  dminxp  4765  imainrect  4766  resdmres  4812  funimacnv  4975  dmaddpi  6423  dmmulpi  6424