Theorem sbcexgOLD 3382

Description: Move existential quantifier in and out of class substitution. (Contributed by NM, 21-May-2004.) Obsolete as of 17-Aug-2018. Use sbcex 3337 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
sbcexgOLD

Distinct variable groups:   ,   ,

Proof of Theorem sbcexgOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. 2
2		dfsbcq2 3330	. . 3
3	2	exbidv 1714	. 2
4		sbex 2207	. 2
5	1, 3, 4	vtoclbg 3168	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818  [.wsbc 3327

This theorem is referenced by:  csbunigOLD  4278  csbxpgOLD  5087  csbrngOLD  5474  onfrALTlem5VD  33685  csbxpgVD  33694  csbrngVD  33696  csbunigVD  33698

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-11 1842  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