Theorem sbcthdv 3343

Description: Deduction version of sbcth 3342. (Contributed by NM, 30-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)

Hypothesis

Ref	Expression
sbcthdv.1

Assertion

Ref	Expression
sbcthdv

Distinct variable group:   ,

Proof of Theorem sbcthdv

Step	Hyp	Ref	Expression
1		sbcthdv.1	. . 3
2	1	alrimiv 1719	. 2
3		spsbc 3340	. 2
4	2, 3	mpan9 469	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-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-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328