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Theorem moa1 2509
 Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 1755 and exa1 1756. (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 2508 1 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃*wmo 2459 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463 This theorem is referenced by: (None)
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