Theorem inteqi 3888

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 3887	. 2 |- ( A = B -> |^| A = |^| B )
3	1, 2	ax-mp 5	1 |- |^| A = |^| B

Syntax hints:   = wceq 1372   |^|cint 3884

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-ral 2488  df-int 3885

This theorem is referenced by:  elintrab  3896  ssintrab  3907  intmin2  3910  intsng  3918  intexrabim  4196  op1stb  4524  bm2.5ii  4543  dfiin3g  4935  op2ndb  5165  bj-dfom  15831  bj-omind  15832