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Theorem r19.27z 3718
 Description: Restricted quantifier version of Theorem 19.27 of [Margaris] p. 90. It is valid only when the domain of quantification is not empty. (Contributed by NM, 26-Oct-2010.)
Hypothesis
Ref Expression
r19.27z.1
Assertion
Ref Expression
r19.27z
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.27z
StepHypRef Expression
1 r19.27z.1 . . . 4
21r19.3rz 3711 . . 3
32anbi2d 685 . 2
4 r19.26 2830 . 2
53, 4syl6rbbr 256 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wne 2598  wral 2697  c0 3620 This theorem is referenced by:  raaan  3727  raaan2  27884 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-ne 2600  df-ral 2702  df-v 2950  df-dif 3315  df-nul 3621
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