New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  r2exf Unicode version

Theorem r2exf 2650
 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 2620 . 2
2 r2alf.1 . . . . . 6
32nfcri 2483 . . . . 5
4319.42 1880 . . . 4
5 anass 630 . . . . 5
65exbii 1582 . . . 4
7 df-rex 2620 . . . . 5
87anbi2i 675 . . . 4
94, 6, 83bitr4i 268 . . 3
109exbii 1582 . 2
111, 10bitr4i 243 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wcel 1710  wnfc 2476  wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620 This theorem is referenced by:  r2ex  2652  rexcomf  2770
 Copyright terms: Public domain W3C validator