Theorem sbcreugOLD 3415

Description: Interchange class substitution and restricted uniqueness quantifier. (Contributed by NM, 24-Feb-2013.) Obsolete as of 18-Aug-2018. Use sbcreu 3414 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
sbcreugOLD

Distinct variable groups:   ,   ,   ,

Proof of Theorem sbcreugOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. 2
2		dfsbcq2 3330	. . 3
3	2	reubidv 3042	. 2
4		nfcv 2619	. . . 4
5		nfs1v 2181	. . . 4
6	4, 5	nfreu 3032	. . 3
7		sbequ12 1992	. . . 4
8	7	reubidv 3042	. . 3
9	6, 8	sbie 2149	. 2
10	1, 3, 9	vtoclbg 3168	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  E!wreu 2809  [.wsbc 3327

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-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-reu 2814  df-v 3111  df-sbc 3328