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Theorem 2sbcrex 35339
 Description: Exchange an existential quantifier with two substitutions. (Contributed by Stefan O'Rear, 11-Oct-2014.) (Revised by NM, 24-Aug-2018.)
Assertion
Ref Expression
2sbcrex
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   ()

Proof of Theorem 2sbcrex
StepHypRef Expression
1 sbcrex 3381 . . 3
21sbcbii 3361 . 2
3 sbcrex 3381 . 2
42, 3bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 187  wrex 2783  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-3an 984  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-rex 2788  df-v 3089  df-sbc 3306 This theorem is referenced by:  2rexfrabdioph  35351  4rexfrabdioph  35353
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