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Theorem r19.44v 3014
Description: One direction of a restricted quantifier version of 19.44 1969. The other direction holds when is nonempty, see r19.44zv 3927. (Contributed by NM, 2-Apr-2004.)
Assertion
Ref Expression
r19.44v
Distinct variable group:   ,

Proof of Theorem r19.44v
StepHypRef Expression
1 r19.43 3013 . 2
2 idd 24 . . . 4
32rexlimiv 2943 . . 3
43orim2i 518 . 2
51, 4sylbi 195 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  e.wcel 1818  E.wrex 2808
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
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-ral 2812  df-rex 2813
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