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Theorem r19.36av 2848
 Description: One direction of a restricted quantifier version of Theorem 19.36 of [Margaris] p. 90. The other direction doesn't hold when is empty. (Contributed by NM, 22-Oct-2003.)
Assertion
Ref Expression
r19.36av
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.36av
StepHypRef Expression
1 r19.35 2847 . 2
2 idd 22 . . . 4
32rexlimiv 2816 . . 3
43imim2i 14 . 2
51, 4sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725  wral 2697  wrex 2698 This theorem is referenced by:  iinss  4134  uniimadom  8411  hashgt12el  11674 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-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-ral 2702  df-rex 2703
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