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Theorem r2alf 2779
 Description: Double restricted universal quantification. (Contributed by Mario Carneiro, 14-Oct-2016.) Use r2allem 2778. (Revised by Wolf Lammen, 9-Jan-2020.)
Hypothesis
Ref Expression
r2alf.1
Assertion
Ref Expression
r2alf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem r2alf
StepHypRef Expression
1 r2alf.1 . . . 4
21nfcri 2557 . . 3
3219.21 1933 . 2
43r2allem 2778 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367  wal 1403   wcel 1842  wnfc 2550  wral 2753 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-ex 1634  df-nf 1638  df-sb 1764  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758 This theorem is referenced by:  r2alOLD  2782  r2exf  2927  ralcomf  2965
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