Theorem sbcimdvOLD 3397

Description: Substitution analog of Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 11-Nov-2005.) Obsolete as of 17-Aug-2018. Use sbcimdv 3396 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
sbcimdv.1

Assertion

Ref	Expression
sbcimdvOLD

Distinct variable group:   ,

Proof of Theorem sbcimdvOLD

Step	Hyp	Ref	Expression
1		sbcimdv.1	. . . . 5
2	1	alrimiv 1719	. . . 4
3		spsbc 3340	. . . 4
4	2, 3	syl5 32	. . 3
5		sbcimg 3369	. . 3
6	4, 5	sylibd 214	. 2
7	6	impcom 430	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  e.wcel 1818  [.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-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