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Theorem rr19.28v 2847
 Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the non-empty class condition of r19.28zv 3455 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 445 . . . . . 6
21ralimi 2580 . . . . 5
3 biidd 230 . . . . . 6
43rcla4v 2817 . . . . 5
52, 4syl5 30 . . . 4
6 simpr 449 . . . . . 6
76ralimi 2580 . . . . 5
87a1i 12 . . . 4
95, 8jcad 521 . . 3
109ralimia 2578 . 2
11 r19.28av 2644 . . 3
1211ralimi 2580 . 2
1310, 12impbii 182 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360   wceq 1619   wcel 1621  wral 2509 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-v 2729
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