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Theorem 2sbcrex 26857
 Description: Exchange an existential quantifier with two substitutions. (Contributed by Stefan O'Rear, 11-Oct-2014.)
Hypotheses
Ref Expression
2sbcrex.1
2sbcrex.2
Assertion
Ref Expression
2sbcrex
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   ()

Proof of Theorem 2sbcrex
StepHypRef Expression
1 2sbcrex.2 . . . 4
2 sbcrexg 3238 . . . 4
31, 2ax-mp 5 . . 3
43sbcbii 3218 . 2
5 2sbcrex.1 . . 3
6 sbcrexg 3238 . . 3
75, 6ax-mp 5 . 2
84, 7bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wcel 1726  wrex 2708  cvv 2958  wsbc 3163 This theorem is referenced by:  2rexfrabdioph  26870  4rexfrabdioph  26872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-sbc 3164
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