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Theorem r2alf 2452
 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 2421 . 2
2 r2alf.1 . . . . . 6
32nfcri 2275 . . . . 5
4319.21 1562 . . . 4
5 impexp 261 . . . . 5
65albii 1446 . . . 4
7 df-ral 2421 . . . . 5
87imbi2i 225 . . . 4
94, 6, 83bitr4i 211 . . 3
109albii 1446 . 2
111, 10bitr4i 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329   wcel 1480  wnfc 2268  wral 2416 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421 This theorem is referenced by:  r2al  2454  ralcomf  2592
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