Theorem inteqi 3610

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 3609	. 2 |- (A = B -> |^|A = |^|B)
3	1, 2	ax-mp 7	1 |- |^|A = |^|B

Syntax hints:   = wceq 1242   |^|cint 3606

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-int 3607

This theorem is referenced by:  elintrab  3618  ssintrab  3629  intmin2  3632  intsng  3640  intexrabim  3898  op1stb  4175  bm2.5ii  4188  dfiin3g  4533  op2ndb  4747  bj-dfom  9392  bj-omind  9393