Theorem eumoi 1405

Description: "At most one" inferred from existential uniqueness.

Hypothesis

Ref	Expression
eumoi.1	|- E!xph

Assertion

Ref	Expression
eumoi	|- E*xph

Proof of Theorem eumoi

Step	Hyp	Ref	Expression
1		eumoi.1	. 2 |- E!xph
2		eumo 1404	. 2 |- (E!xph -> E*xph)
3	1, 2	ax-mp 7	1 |- E*xph

Syntax hints:  E!weu 1373  E*wmo 1374

This theorem is referenced by:  euxfr 1917

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376

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