Theorem exmoeu2 1416

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 1411	. 2 |- (E!xph <-> (E.xph /\ E*xph))
2	1	baibr 688	1 |- (E.xph -> (E*xph <-> E!xph))

Syntax hints:   -> wi 3   <-> wb 146  E.wex 982  E!weu 1382  E*wmo 1383

This theorem is referenced by:  euim 1423

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385

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