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Theorem moani 2680
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 2679 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
31, 2ax-mp 5 1 ∃*𝑥(𝜓𝜑)
Colors of variables: wff setvar class
Syntax hints:  wa 385  ∃*wmo 2589
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006
This theorem depends on definitions:  df-bi 199  df-an 386  df-ex 1876  df-mo 2591
This theorem is referenced by:  euxfr2  3587  rmoeq  3603  reuxfr2d  5089  fvopab6  6536  1stconst  7502  2ndconst  7503  iunmapdisj  9132  axaddf  10254  axmulf  10255  joinval  17320  meetval  17334  reuxfr3d  29852
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