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Theorem reurmo 2826
Description: Restricted existential uniqueness implies restricted "at most one." (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
reurmo (∃!x A φ∃*x A φ)

Proof of Theorem reurmo
StepHypRef Expression
1 reu5 2824 . 2 (∃!x A φ ↔ (x A φ ∃*x A φ))
21simprbi 450 1 (∃!x A φ∃*x A φ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wrex 2615  ∃!wreu 2616  ∃*wrmo 2617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-rex 2620  df-reu 2621  df-rmo 2622
This theorem is referenced by: (None)
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