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Theorem moan 2626
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 479 . 2 ((𝜓𝜑) → 𝜑)
21moimi 2622 1 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  ∃*wmo 2572
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-10 2132  ax-12 2160
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1818  df-nf 1823  df-eu 2575  df-mo 2576
This theorem is referenced by:  moani  2627  mooran1  2629  moanim  2631  mormo  3261  rmoan  3512
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