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Theorem moa1 2629
Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 1807 and exa1 1831. (Contributed by NM, 28-Jul-1995.) (Proof shortened by Wolf Lammen, 22-Dec-2018.) (Revised by BJ, 29-Mar-2021.)
Assertion
Ref Expression
moa1 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)

Proof of Theorem moa1
StepHypRef Expression
1 ax-1 6 . 2 (𝜓 → (𝜑𝜓))
21moimi 2621 1 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃*wmo 2614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803
This theorem depends on definitions:  df-bi 209  df-ex 1774  df-mo 2616
This theorem is referenced by: (None)
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