Theorem inteqi 3848

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 3847	. 2 |- ( A = B -> |^| A = |^| B )
3	1, 2	ax-mp 5	1 |- |^| A = |^| B

Syntax hints:   = wceq 1353   |^|cint 3844

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-int 3845

This theorem is referenced by:  elintrab  3856  ssintrab  3867  intmin2  3870  intsng  3878  intexrabim  4152  op1stb  4477  bm2.5ii  4494  dfiin3g  4883  op2ndb  5110  bj-dfom  14536  bj-omind  14537