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Theorem rr19.28v 3242
Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the nonempty class condition of r19.28zv 3924 when there is an outer quantifier. (Contributed by NM, 29-Oct-2012.)
Assertion
Ref Expression
rr19.28v
Distinct variable groups:   ,   ,   ,

Proof of Theorem rr19.28v
StepHypRef Expression
1 simpl 457 . . . . . 6
21ralimi 2850 . . . . 5
3 biidd 237 . . . . . 6
43rspcv 3206 . . . . 5
52, 4syl5 32 . . . 4
6 simpr 461 . . . . . 6
76ralimi 2850 . . . . 5
87a1i 11 . . . 4
95, 8jcad 533 . . 3
109ralimia 2848 . 2
11 r19.28v 2991 . . 3
1211ralimi 2850 . 2
1310, 12impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  A.wral 2807
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111
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