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Theorem r2exf 2741
 Description: Double restricted existential quantification. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypothesis
Ref Expression
r2alf.1
Assertion
Ref Expression
r2exf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem r2exf
StepHypRef Expression
1 df-rex 2711 . 2
2 r2alf.1 . . . . . 6
32nfcri 2566 . . . . 5
4319.42 1902 . . . 4
5 anass 631 . . . . 5
65exbii 1592 . . . 4
7 df-rex 2711 . . . . 5
87anbi2i 676 . . . 4
94, 6, 83bitr4i 269 . . 3
109exbii 1592 . 2
111, 10bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wcel 1725  wnfc 2559  wrex 2706 This theorem is referenced by:  r2ex  2743  rexcomf  2867 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711
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