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Theorem r19.37zv 3492
 Description: Restricted quantifier version of Theorem 19.37 of [Margaris] p. 90. It is valid only when the domain of quantification is not empty. (Contributed by Paul Chapman, 8-Oct-2007.)
Assertion
Ref Expression
r19.37zv
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem r19.37zv
StepHypRef Expression
1 r19.3rzv 3489 . . 3
21imbi1d 310 . 2
3 r19.35 2658 . 2
42, 3syl6rbbr 257 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wne 2419  wral 2516  wrex 2517  c0 3397 This theorem is referenced by:  ishlat3N  28674  hlsupr2  28706 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 1927  ax-ext 2237 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 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2520  df-rex 2521  df-v 2742  df-dif 3097  df-nul 3398
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