Theorem exmoeu2 1414

Description: Existence implies "at most one" is equivalent to uniqueness.

Assertion

Ref	Expression
exmoeu2	|- (E.xph -> (E*xph <-> E!xph))

Proof of Theorem exmoeu2

Step	Hyp	Ref	Expression
1		eu5 1409	. 2 |- (E!xph <-> (E.xph /\ E*xph))
2	1	baibr 686	1 |- (E.xph -> (E*xph <-> E!xph))

Syntax hints:   -> wi 3   <-> wb 146  E.wex 980  E!weu 1380  E*wmo 1381

This theorem is referenced by:  euim 1421

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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