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Theorem moan 2673
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moan (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))

Proof of Theorem moan
StepHypRef Expression
1 simpr 471 . 2 ((𝜓𝜑) → 𝜑)
21moimi 2669 1 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  ∃*wmo 2619
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-ex 1853  df-nf 1858  df-eu 2622  df-mo 2623
This theorem is referenced by:  moani  2674  mooran1  2676  moanim  2678  mormo  3307  rmoan  3558
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