MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  moani Structured version   Visualization version   GIF version

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
  Copyright terms: Public domain W3C validator