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Theorem r19.37zv 3925
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:   ,   ,

Proof of Theorem r19.37zv
StepHypRef Expression
1 r19.3rzv 3922 . . 3
21imbi1d 317 . 2
3 r19.35 3004 . 2
42, 3syl6rbbr 264 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =/=wne 2652  A.wral 2807  E.wrex 2808   c0 3784
This theorem is referenced by:  ishlat3N  35079  hlsupr2  35111
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-or 370  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-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-nul 3785
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