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Theorem rexcom4b 3131
 Description: Specialized existential commutation lemma. (Contributed by Jeff Madsen, 1-Jun-2011.)
Hypothesis
Ref Expression
rexcom4b.1
Assertion
Ref Expression
rexcom4b
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rexcom4b
StepHypRef Expression
1 rexcom4a 3130 . 2
2 rexcom4b.1 . . . . 5
32isseti 3115 . . . 4
43biantru 505 . . 3
54rexbii 2959 . 2
61, 5bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1395  wex 1613   wcel 1819  wrex 2808  cvv 3109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111 This theorem is referenced by:  islshpat  34928
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