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Theorem moani 1970
 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 1969 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
31, 2ax-mp 7 1 ∃*𝑥(𝜓𝜑)
 Colors of variables: wff set class Syntax hints:   ∧ wa 97  ∃*wmo 1901 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904 This theorem is referenced by:  euxfr2dc  2726  fvopab6  5264  1stconst  5842  2ndconst  5843
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