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Theorem ralbinrald 27844
 Description: Elemination of a restricted universal quantification under certain conditions. (Contributed by Alexander van der Vekens, 2-Aug-2017.)
Hypotheses
Ref Expression
ralbinrald.1
ralbinrald.2
ralbinrald.3
Assertion
Ref Expression
ralbinrald
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ralbinrald
StepHypRef Expression
1 ralbinrald.1 . . 3
2 ralbinrald.3 . . . 4
32adantl 453 . . 3
41, 3rspcdv 3015 . 2
5 ralbinrald.2 . . . . . 6
62bicomd 193 . . . . . 6
75, 6syl 16 . . . . 5
87adantl 453 . . . 4
98biimpd 199 . . 3
109ralrimdva 2756 . 2
114, 10impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1649   wcel 1721  wral 2666 This theorem is referenced by:  dfdfat2  27862 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-v 2918
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