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Theorem r2exf 2359
 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 2329 . 2
2 r2alf.1 . . . . . 6
32nfcri 2188 . . . . 5
4319.42 1594 . . . 4
5 anass 387 . . . . 5
65exbii 1512 . . . 4
7 df-rex 2329 . . . . 5
87anbi2i 438 . . . 4
94, 6, 83bitr4i 205 . . 3
109exbii 1512 . 2
111, 10bitr4i 180 1
 Colors of variables: wff set class Syntax hints:   wa 101   wb 102  wex 1397   wcel 1409  wnfc 2181  wrex 2324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329 This theorem is referenced by:  r2ex  2361  rexcomf  2489
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