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Theorem moani 2096
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 2095 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
31, 2ax-mp 5 1 ∃*𝑥(𝜓𝜑)
Colors of variables: wff set class
Syntax hints:  wa 104  ∃*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by:  euxfr2dc  2922  fvopab6  5612  1stconst  6221  2ndconst  6222  axaddf  7866  axmulf  7867
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