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Theorem moimdv 2563
 Description: The at-most-one quantifier reverses implication, deduction form. (Contributed by Thierry Arnoux, 25-Feb-2017.)
Hypothesis
Ref Expression
moimdv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
moimdv (𝜑 → (∃*𝑥𝜒 → ∃*𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem moimdv
StepHypRef Expression
1 moimdv.1 . . 3 (𝜑 → (𝜓𝜒))
21alrimiv 1928 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
3 moim 2561 . 2 (∀𝑥(𝜓𝜒) → (∃*𝑥𝜒 → ∃*𝑥𝜓))
42, 3syl 17 1 (𝜑 → (∃*𝑥𝜒 → ∃*𝑥𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  ∃*wmo 2555 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911 This theorem depends on definitions:  df-bi 210  df-ex 1782  df-mo 2557 This theorem is referenced by:  disjss1  5007  brdom6disj  10005  funressnfv  44046  funressnvmo  44048
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