Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rr19.28v Unicode version

Theorem rr19.28v 2910
 Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the non-empty class condition of r19.28zv 3549 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 2618 . . . . 5
3 biidd 228 . . . . . 6
43rspcv 2880 . . . . 5
52, 4syl5 28 . . . 4
6 simpr 447 . . . . . 6
76ralimi 2618 . . . . 5
87a1i 10 . . . 4
95, 8jcad 519 . . 3
109ralimia 2616 . 2
11 r19.28av 2682 . . 3
1211ralimi 2618 . 2
1310, 12impbii 180 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1623   wcel 1684  wral 2543 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-v 2790
 Copyright terms: Public domain W3C validator