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Theorem 2sbcrex 26733
 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 3196 . . . 4
31, 2ax-mp 8 . . 3
43sbcbii 3176 . 2
5 2sbcrex.1 . . 3
6 sbcrexg 3196 . . 3
75, 6ax-mp 8 . 2
84, 7bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wcel 1721  wrex 2667  cvv 2916  wsbc 3121 This theorem is referenced by:  2rexfrabdioph  26746  4rexfrabdioph  26748 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-v 2918  df-sbc 3122
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