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Theorem rexcom13 3020
Description: Swap first and third restricted existential quantifiers. (Contributed by NM, 8-Apr-2015.)
Assertion
Ref Expression
rexcom13
Distinct variable groups:   , ,   , ,   , ,

Proof of Theorem rexcom13
StepHypRef Expression
1 rexcom 3019 . 2
2 rexcom 3019 . . 3
32rexbii 2959 . 2
4 rexcom 3019 . 2
51, 3, 43bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  E.wrex 2808
This theorem is referenced by:  rexrot4  3021
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813
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