Theorem sbc6 3354

Description: An equivalence for class substitution. (Contributed by NM, 23-Aug-1993.) (Proof shortened by Eric Schmidt, 17-Jan-2007.)

Hypothesis

Ref	Expression
sbc6.1

Assertion

Ref	Expression
sbc6

Distinct variable group:   ,

Proof of Theorem sbc6

Step	Hyp	Ref	Expression
1		sbc6.1	. 2
2		sbc6g 3353	. 2
3	1, 2	ax-mp 5	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  cvv 3109  [.wsbc 3327

This theorem is referenced by:  intab  4317  2sbc6g  31322

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328