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Theorem nrexrmo 2829
Description: Nonexistence implies restricted "at most one". (Contributed by NM, 17-Jun-2017.)
Assertion
Ref Expression
nrexrmo x A φ∃*x A φ)

Proof of Theorem nrexrmo
StepHypRef Expression
1 pm2.21 100 . 2 x A φ → (x A φ∃!x A φ))
2 rmo5 2828 . 2 (∃*x A φ ↔ (x A φ∃!x A φ))
31, 2sylibr 203 1 x A φ∃*x A φ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wrex 2616  ∃!wreu 2617  ∃*wrmo 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-mo 2209  df-rex 2621  df-reu 2622  df-rmo 2623
This theorem is referenced by: (None)
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