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Theorem r19.37zv 3688
 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 3685 . . 3
21imbi1d 309 . 2
3 r19.35 2819 . 2
42, 3syl6rbbr 256 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wne 2571  wral 2670  wrex 2671  c0 3592 This theorem is referenced by:  ishlat3N  29841  hlsupr2  29873 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-v 2922  df-dif 3287  df-nul 3593
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