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Theorem exim 1575
 Description: Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 4-Jul-2014.)
Assertion
Ref Expression
exim (x(φψ) → (xφxψ))

Proof of Theorem exim
StepHypRef Expression
1 con3 126 . . . 4 ((φψ) → (¬ ψ → ¬ φ))
21al2imi 1561 . . 3 (x(φψ) → (x ¬ ψx ¬ φ))
3 alnex 1543 . . 3 (x ¬ ψ ↔ ¬ xψ)
4 alnex 1543 . . 3 (x ¬ φ ↔ ¬ xφ)
52, 3, 43imtr3g 260 . 2 (x(φψ) → (¬ xψ → ¬ xφ))
65con4d 97 1 (x(φψ) → (xφxψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀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 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  eximi  1576  exbi  1581  eximdh  1588  19.29  1596  19.25  1603  19.30  1604  19.23t  1800  19.23tOLD  1819  19.23hOLD  1820  2mo  2282  elex22  2870  elex2  2871  vtoclegft  2926  spcimgft  2930
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