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Theorem sbcth2 3389
 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:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcth2
StepHypRef Expression
1 sbcth2.1 . . 3
21rgen 2792 . 2
3 rspsbc 3384 . 2
42, 3mpi 21 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1870  wral 2782  wsbc 3305 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-v 3089  df-sbc 3306 This theorem is referenced by: (None)
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