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Theorem moa1 2504
Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 1753 and exa1 1754. (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 2503 1 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃*wmo 2454
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-12 2031
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-eu 2457  df-mo 2458
This theorem is referenced by: (None)
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