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Theorem exan 1973
Description: Place a conjunct in the scope of an existential quantifier. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.)
Hypothesis
Ref Expression
exan.1
Assertion
Ref Expression
exan

Proof of Theorem exan
StepHypRef Expression
1 exan.1 . 2
21simpri 462 . . . 4
32nfth 1625 . . 3
4319.41 1971 . 2
51, 4mpbir 209 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  E.wex 1612
This theorem is referenced by:  bm1.3ii  4576  ac6s6f  30581  fnchoice  31404
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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