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Theorem moa1 2520
 Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 1738 and exa1 1762. (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 2519 1 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃*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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