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Theorem r19.36av 2650
 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 2649 . 2
2 idd 23 . . . 4
32rexlimiv 2623 . . 3
43imim2i 15 . 2
51, 4sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 6   wcel 1621  wral 2509  wrex 2510 This theorem is referenced by:  iinss  3851  uniimadom  8050 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-gen 1536  ax-17 1628  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-ral 2513  df-rex 2514
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