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Theorem r2alf 2875
 Description: Double restricted universal quantification. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypothesis
Ref Expression
r2alf.1
Assertion
Ref Expression
r2alf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem r2alf
StepHypRef Expression
1 df-ral 2804 . 2
2 r2alf.1 . . . . . 6
32nfcri 2609 . . . . 5
4319.21 1844 . . . 4
5 impexp 446 . . . . 5
65albii 1611 . . . 4
7 df-ral 2804 . . . . 5
87imbi2i 312 . . . 4
94, 6, 83bitr4i 277 . . 3
109albii 1611 . 2
111, 10bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1368   wcel 1758  wnfc 2602  wral 2799 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1588  df-nf 1591  df-sb 1703  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2804 This theorem is referenced by:  r2al  2877  ralcomf  2985
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