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Theorem moani 2631
 Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
moani.1 ∃*𝑥𝜑
Assertion
Ref Expression
moani ∃*𝑥(𝜓𝜑)

Proof of Theorem moani
StepHypRef Expression
1 moani.1 . 2 ∃*𝑥𝜑
2 moan 2630 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
31, 2ax-mp 5 1 ∃*𝑥(𝜓𝜑)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 398  ∃*wmo 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803 This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1774  df-mo 2616 This theorem is referenced by:  euxfr2w  3709  euxfr2  3711  rmoeq  3727  reuxfrd  3737  fvopab6  6794  1stconst  7787  2ndconst  7788  iunmapdisj  9441  axaddf  10559  axmulf  10560  joinval  17607  meetval  17621  reuxfrdf  30247
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