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

Theorem moani 2512
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 2511 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
31, 2ax-mp 5 1 ∃*𝑥(𝜓𝜑)
Colors of variables: wff setvar class
Syntax hints:  wa 382  ∃*wmo 2458
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-eu 2461  df-mo 2462
This theorem is referenced by:  euxfr2  3357  rmoeq  3371  reuxfr2d  4812  fvopab6  6203  1stconst  7129  2ndconst  7130  iunmapdisj  8706  axaddf  9822  axmulf  9823  joinval  16774  meetval  16788  reuxfr3d  28519
  Copyright terms: Public domain W3C validator