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Theorem moimd 29172
Description: "At most one" is preserved through implication (notice wff reversal). (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 1852 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
3 moim 2518 . 2 (∀𝑥(𝜓𝜒) → (∃*𝑥𝜒 → ∃*𝑥𝜓))
42, 3syl 17 1 (𝜑 → (∃*𝑥𝜒 → ∃*𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  ∃*wmo 2470
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-eu 2473  df-mo 2474
This theorem is referenced by: (None)
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