Theorem sbcth2 3422

Description: A substitution into a theorem. (Contributed by NM, 1-Mar-2008.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)

Hypothesis

Ref	Expression
sbcth2.1

Assertion

Ref	Expression
sbcth2

Distinct variable group:   ,

Proof of Theorem sbcth2

Step	Hyp	Ref	Expression
1		sbcth2.1	. . 3
2	1	rgen 2817	. 2
3		rspsbc 3417	. 2
4	2, 3	mpi 17	1

Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  [.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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-sbc 3328