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Theorem r19.36av 3004
 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 3003 . 2
2 idd 24 . . . 4
32rexlimiv 2944 . . 3
43imim2i 14 . 2
51, 4sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1762  wral 2809  wrex 2810 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-ral 2814  df-rex 2815 This theorem is referenced by:  iinss  4371  uniimadom  8910  hashgt12el  12435
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