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Theorem r19.27av 2995
 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 6 . . . 4
21ralrimiv 2876 . . 3
32anim2i 569 . 2
4 r19.26 2989 . 2
53, 4sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wcel 1767  wral 2814 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680 This theorem depends on definitions:  df-bi 185  df-an 371  df-ral 2819 This theorem is referenced by:  r19.28av  2996  txlm  19912  tx1stc  19914  spanuni  26166
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