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Theorem moa1 2685
Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 1901 and exa1 1925. (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 2683 1 (∃*𝑥(𝜑𝜓) → ∃*𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃*wmo 2633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1880  ax-4 1897  ax-5 2004  ax-6 2070  ax-7 2106  ax-10 2187  ax-12 2216
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-ex 1860  df-nf 1865  df-eu 2636  df-mo 2637
This theorem is referenced by: (None)
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