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Theorem exlimd 1806
 Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
exlimd.1 xφ
exlimd.2 xχ
exlimd.3 (φ → (ψχ))
Assertion
Ref Expression
exlimd (φ → (xψχ))

Proof of Theorem exlimd
StepHypRef Expression
1 exlimd.1 . . 3 xφ
2 exlimd.3 . . 3 (φ → (ψχ))
31, 2alrimi 1765 . 2 (φx(ψχ))
4 exlimd.2 . . 3 xχ
5419.23 1801 . 2 (x(ψχ) ↔ (xψχ))
63, 5sylib 188 1 (φ → (xψχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544 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-ex 1542  df-nf 1545 This theorem is referenced by:  exlimdh  1807  exlimdd  1889  equs5  1996  exists2  2294  ceqsalg  2883  copsex2t  4608  mosubopt  4612  ov3  5599
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