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Theorem euimmo 2660
 Description: Uniqueness implies "at most one" through reverse implication. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
euimmo (∀𝑥(𝜑𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑))

Proof of Theorem euimmo
StepHypRef Expression
1 eumo 2636 . 2 (∃!𝑥𝜓 → ∃*𝑥𝜓)
2 moim 2657 . 2 (∀𝑥(𝜑𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑))
31, 2syl5 34 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1630  ∃!weu 2607  ∃*wmo 2608 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  ax-7 2090  ax-10 2168  ax-12 2196 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-eu 2611  df-mo 2612 This theorem is referenced by:  euim  2661  2eumo  2683  moeq3  3524  reuss2  4050
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