Theorem ineq2i 3454

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 3451	. 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 1642   i^i cin 3208

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213

This theorem is referenced by:  in4  3471  inindir  3473  indif2  3498  difun1  3514  dfrab3ss  3533  undif1  3625  difdifdir  3637  dfif3  3672  dfif5  3674  intunsn  3965  rint0  3966  riin0  4039  inindif  4075  ssfin  4470  spfinex  4537  res0  4977  resres  4980  resundi  4981  resindi  4983  inres  4985  resopab  4999  dminxp  5061  resdmres  5078  funimacnv  5168  sbthlem1  6203