Theorem inteqi 3660

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 3659	. 2 |- ( A = B -> |^| A = |^| B )
3	1, 2	ax-mp 7	1 |- |^| A = |^| B

Syntax hints:   = wceq 1285   |^|cint 3656

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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-int 3657

This theorem is referenced by:  elintrab  3668  ssintrab  3679  intmin2  3682  intsng  3690  intexrabim  3948  op1stb  4255  bm2.5ii  4268  dfiin3g  4638  op2ndb  4854  bj-dfom  10995  bj-omind  10996