Theorem exmoeu2 1040

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 1035	. 2 |- (E!xph <-> (E.xph /\ E*xph))
2	1	baibr 507	1 |- (E.xph -> (E*xph <-> E!xph))

Syntax hints:   -> wi 2   <-> wb 127  E.wex 678  E!weu 1007  E*wmo 1008

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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