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Theorem r19.28z 3452
 Description: Restricted quantifier version of Theorem 19.28 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
r19.3rz.1
Assertion
Ref Expression
r19.28z
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.28z
StepHypRef Expression
1 r19.3rz.1 . . . 4
21r19.3rz 3451 . . 3
32anbi1d 688 . 2
4 r19.26 2637 . 2
53, 4syl6rbbr 257 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wnf 1539   wne 2412  wral 2509  c0 3362 This theorem is referenced by:  raaan  3467 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-ne 2414  df-ral 2513  df-v 2729  df-dif 3081  df-nul 3363
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