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Theorem 19.35 1599
 Description: Theorem 19.35 of [Margaris] p. 90. This theorem is useful for moving an implication (in the form of the right-hand side) into the scope of a single existential quantifier. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 27-Jun-2014.)
Assertion
Ref Expression
19.35

Proof of Theorem 19.35
StepHypRef Expression
1 19.26 1592 . . . 4
2 annim 416 . . . . 5
32albii 1554 . . . 4
4 alnex 1569 . . . . 5
54anbi2i 678 . . . 4
61, 3, 53bitr3i 268 . . 3
7 alnex 1569 . . 3
8 annim 416 . . 3
96, 7, 83bitr3i 268 . 2
109con4bii 290 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wa 360  wal 1532  wex 1537 This theorem is referenced by:  19.35i  1600  19.35ri  1601  19.25  1602  19.43  1604  19.36  1788  19.37  1790  19.39  1792  19.24  1793  sbequi  1951  grothprim  8336 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
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