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Theorem r19.27av 2643
 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 7 . . . 4
21ralrimiv 2587 . . 3
32anim2i 555 . 2
4 r19.26 2637 . 2
53, 4sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360   wcel 1621  wral 2509 This theorem is referenced by:  r19.28av  2644  txlm  17174  tx1stc  17176  spanuni  21953  tartarmap  25054 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1540  df-ral 2513
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