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Theorem r19.27v 2990
Description: Restricted quantitifer version of one direction of 19.27 1923. (The other direction holds when is nonempty, see r19.27zv 3929.) (Contributed by NM, 3-Jun-2004.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.27v
Distinct variable group:   ,

Proof of Theorem r19.27v
StepHypRef Expression
1 ax-1 6 . . . 4
21ralrimiv 2869 . . 3
32anim2i 569 . 2
4 r19.26 2984 . 2
53, 4sylibr 212 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  A.wral 2807
This theorem is referenced by:  r19.28v  2991  txlm  20149  tx1stc  20151  spanuni  26462
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-an 371  df-ral 2812
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