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Theorem eumoi 2184
Description: "At most one" inferred from existential uniqueness. (Contributed by NM, 5-Apr-1995.)
Hypothesis
Ref Expression
eumoi.1  |-  E! x ph
Assertion
Ref Expression
eumoi  |-  E* x ph

Proof of Theorem eumoi
StepHypRef Expression
1 eumoi.1 . 2  |-  E! x ph
2 eumo 2183 . 2  |-  ( E! x ph  ->  E* x ph )
31, 2ax-mp 8 1  |-  E* x ph
Colors of variables: wff set class
Syntax hints:   E!weu 2143   E*wmo 2144
This theorem is referenced by:  euxfr  2951
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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