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

Theorem moan 2632
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moan (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))

Proof of Theorem moan
StepHypRef Expression
1 simpr 487 . 2 ((𝜓𝜑) → 𝜑)
21moimi 2623 1 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  ∃*wmo 2616
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-mo 2618
This theorem is referenced by:  moani  2633  mooran1  2635  moanimlem  2699  mormo  3430  rmoan  3730
  Copyright terms: Public domain W3C validator