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Theorem reurmo 3300
Description: Restricted existential uniqueness implies restricted "at most one." (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
reurmo (∃!𝑥𝐴 𝜑 → ∃*𝑥𝐴 𝜑)

Proof of Theorem reurmo
StepHypRef Expression
1 reu5 3298 . 2 (∃!𝑥𝐴 𝜑 ↔ (∃𝑥𝐴 𝜑 ∧ ∃*𝑥𝐴 𝜑))
21simprbi 483 1 (∃!𝑥𝐴 𝜑 → ∃*𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wrex 3051  ∃!wreu 3052  ∃*wrmo 3053
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-eu 2611  df-mo 2612  df-rex 3056  df-reu 3057  df-rmo 3058
This theorem is referenced by:  reuxfrd  5042  enqeq  9948  eqsqrtd  14306  efgred2  18366  0frgp  18392  frgpnabllem2  18477  frgpcyg  20124  lmieu  25875  reuxfr4d  29638  poimirlem25  33747  poimirlem26  33748  reuimrmo  41684  2reurmo  41688  2rexreu  41691  2reu2  41693
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