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Theorem r19.37 2939
 Description: Restricted quantifier version of one direction of 19.37 2046. (The other direction does not hold when is empty.) (Contributed by FL, 13-May-2012.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypothesis
Ref Expression
r19.37.1
Assertion
Ref Expression
r19.37

Proof of Theorem r19.37
StepHypRef Expression
1 r19.35 2937 . 2
2 r19.37.1 . . . 4
3 ax-1 6 . . . 4
42, 3ralrimi 2788 . . 3
54imim1i 60 . 2
61, 5sylbi 199 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wnf 1667   wcel 1887  wral 2737  wrex 2738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668  df-ral 2742  df-rex 2743 This theorem is referenced by:  r19.37v  2940  ss2iundf  36251
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