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Theorem moan 2699
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 473 . 2 ((𝜓𝜑) → 𝜑)
21moimi 2694 1 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  ∃*wmo 2633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1860  df-mo 2635
This theorem is referenced by:  moani  2700  mooran1  2702  moanim  2704  mormo  3358  rmoan  3615
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