Theorem inteqi 3903

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 3902	. 2 |- ( A = B -> |^| A = |^| B )
3	1, 2	ax-mp 5	1 |- |^| A = |^| B

Syntax hints:   = wceq 1373   |^|cint 3899

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-ral 2491  df-int 3900

This theorem is referenced by:  elintrab  3911  ssintrab  3922  intmin2  3925  intsng  3933  intexrabim  4213  op1stb  4543  bm2.5ii  4562  dfiin3g  4955  op2ndb  5185  bj-dfom  16068  bj-omind  16069