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Theorem r19.27av 2836
 Description: Restricted version of one direction of Theorem 19.27 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by NM, 3-Jun-2004.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.27av
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.27av
StepHypRef Expression
1 ax-1 5 . . . 4
21ralrimiv 2780 . . 3
32anim2i 553 . 2
4 r19.26 2830 . 2
53, 4sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725  wral 2697 This theorem is referenced by:  r19.28av  2837  txlm  17668  tx1stc  17670  spanuni  23034 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-ral 2702
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