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Theorem r19.36av 2557
 Description: One direction of a restricted quantifier version of Theorem 19.36 of [Margaris] p. 90. In classical logic, the converse would hold if has at least one element, but in intuitionistic logic, that is not a sufficient condition. (Contributed by NM, 22-Oct-2003.)
Assertion
Ref Expression
r19.36av
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.36av
StepHypRef Expression
1 r19.35-1 2556 . 2
2 idd 21 . . . 4
32rexlimiv 2518 . . 3
43imim2i 12 . 2
51, 4syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1463  wral 2391  wrex 2392 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497  ax-i5r 1498 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-ral 2396  df-rex 2397 This theorem is referenced by:  iinss  3832
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