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Theorem moan 2511
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 475 . 2 ((𝜓𝜑) → 𝜑)
21moimi 2507 1 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  ∃*wmo 2458
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-12 2033
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 2461  df-mo 2462
This theorem is referenced by:  moani  2512  mooran1  2514  moanim  2516  mormo  3134  rmoan  3372
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