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Theorem rr19.28v 3070
 Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the non-empty class condition of r19.28zv 3715 when there is an outer quantifier. (Contributed by NM, 29-Oct-2012.)
Assertion
Ref Expression
rr19.28v
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem rr19.28v
StepHypRef Expression
1 simpl 444 . . . . . 6
21ralimi 2773 . . . . 5
3 biidd 229 . . . . . 6
43rspcv 3040 . . . . 5
52, 4syl5 30 . . . 4
6 simpr 448 . . . . . 6
76ralimi 2773 . . . . 5
87a1i 11 . . . 4
95, 8jcad 520 . . 3
109ralimia 2771 . 2
11 r19.28av 2837 . . 3
1211ralimi 2773 . 2
1310, 12impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wcel 1725  wral 2697 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950
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