Theorem inteqi 1969

Description: Equality inference for class intersection.

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 1968	. 2 |- (A = B -> |^|A = |^|B)
3	1, 2	ax-mp 6	1 |- |^|A = |^|B

Syntax hints:   = wceq 1091  |^|cint 1965

This theorem is referenced by:  elintrab 1977  intmin2 1984  intexrab 1988  intsn 1991  op1stb 1992  bm2.5ii 2274  op2ndb 2638  oawordeulem 3156  rankval2 3514  ranksn 3532  cf0 3705

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-ral 1205  df-int 1966

metamath.org