Theorem eumoi 1412

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 1411	. 2 |- (E!xph -> E*xph)
3	1, 2	ax-mp 7	1 |- E*xph

Syntax hints:  E!weu 1380  E*wmo 1381

This theorem is referenced by:  euxfr 1927

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383

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