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Theorem 2sbcrex 26030
 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.1 . . 3
2 2sbcrex.2 . . . . 5
3 sbcrexg 2996 . . . . 5
42, 3ax-mp 10 . . . 4
54sbcbiiOLD 2977 . . 3
61, 5ax-mp 10 . 2
7 sbcrexg 2996 . . 3
81, 7ax-mp 10 . 2
96, 8bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wcel 1621  wrex 2510  cvv 2727  wsbc 2921 This theorem is referenced by:  2rexfrabdioph  26043  4rexfrabdioph  26045 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514  df-v 2729  df-sbc 2922
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