Theorem inteqi 3775

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 3774	. 2 |- ( A = B -> |^| A = |^| B )
3	1, 2	ax-mp 5	1 |- |^| A = |^| B

Syntax hints:   = wceq 1331   |^|cint 3771

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-int 3772

This theorem is referenced by:  elintrab  3783  ssintrab  3794  intmin2  3797  intsng  3805  intexrabim  4078  op1stb  4399  bm2.5ii  4412  dfiin3g  4797  op2ndb  5022  bj-dfom  13131  bj-omind  13132