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Theorem exan 1882
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.)
Hypothesis
Ref Expression
exan.1 (xφ ψ)
Assertion
Ref Expression
exan x(φ ψ)

Proof of Theorem exan
StepHypRef Expression
1 nfe1 1732 . . . 4 xxφ
2119.28 1870 . . 3 (x(xφ ψ) ↔ (xφ xψ))
3 exan.1 . . 3 (xφ ψ)
42, 3mpgbi 1549 . 2 (xφ xψ)
5 19.29r 1597 . 2 ((xφ xψ) → x(φ ψ))
64, 5ax-mp 5 1 x(φ ψ)
Colors of variables: wff setvar class
Syntax hints:   wa 358  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
This theorem is referenced by: (None)
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