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Theorem rr19.28v 2981
 Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the nonempty class condition of r19.28zv 3645 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 443 . . . . . 6
21ralimi 2689 . . . . 5
3 biidd 228 . . . . . 6
43rspcv 2951 . . . . 5
52, 4syl5 28 . . . 4
6 simpr 447 . . . . . 6
76ralimi 2689 . . . . 5
87a1i 10 . . . 4
95, 8jcad 519 . . 3
109ralimia 2687 . 2
11 r19.28av 2753 . . 3
1211ralimi 2689 . 2
1310, 12impbii 180 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861 This theorem is referenced by: (None)
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