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Theorem moimd 2641
Description: The at-most-one quantifier reverses implication, deduction form. (Contributed by Thierry Arnoux, 25-Feb-2017.)
Hypothesis
Ref Expression
moimd.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
moimd (𝜑 → (∃*𝑥𝜒 → ∃*𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem moimd
StepHypRef Expression
1 moimd.1 . . 3 (𝜑 → (𝜓𝜒))
21alrimiv 2022 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
3 moim 2639 . 2 (∀𝑥(𝜓𝜒) → (∃*𝑥𝜒 → ∃*𝑥𝜓))
42, 3syl 17 1 (𝜑 → (∃*𝑥𝜒 → ∃*𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  ∃*wmo 2562
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005
This theorem depends on definitions:  df-bi 198  df-ex 1875  df-mo 2564
This theorem is referenced by:  disjss1  4782  brdom6disj  9606  funressnfv  41752  funressnvmo  41754  funressnvmoOLD  41755
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