Theorem sbcbig 3374

Description: Distribution of class substitution over biconditional. (Contributed by Raph Levien, 10-Apr-2004.)

Assertion

Ref	Expression
sbcbig

Proof of Theorem sbcbig

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. 2
2		dfsbcq2 3330	. . 3
3		dfsbcq2 3330	. . 3
4	2, 3	bibi12d 321	. 2
5		sbbi 2142	. 2
6	1, 4, 5	vtoclbg 3168	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327

This theorem is referenced by:  sbcbi1  3377  sbcabel  3416  sbcbi  33310  sbc3orgVD  33651  sbcbiVD  33676  bnj89  33774  bj-sbeq  34468  bj-sbceqgALT  34469

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-or 370  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