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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
StepHypRef Expression
1 sbcth2.1 . . 3
21rgen 2817 . 2
3 rspsbc 3417 . 2
42, 3mpi 17 1
 Colors of variables: wff setvar class 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
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