Theorem inteqi 3692

Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003.)

Hypothesis

Ref	Expression
inteqi.1	|- A = B

Assertion

Ref	Expression
inteqi	|- |^| A = |^| B

Proof of Theorem inteqi

Step	Hyp	Ref	Expression
1		inteqi.1	. 2 |- A = B
2		inteq 3691	. 2 |- ( A = B -> |^| A = |^| B )
3	1, 2	ax-mp 7	1 |- |^| A = |^| B

Syntax hints:   = wceq 1289   |^|cint 3688

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-int 3689

This theorem is referenced by:  elintrab  3700  ssintrab  3711  intmin2  3714  intsng  3722  intexrabim  3989  op1stb  4300  bm2.5ii  4313  dfiin3g  4691  op2ndb  4914  bj-dfom  11828  bj-omind  11829