Theorem eumo 1037

Description: Existential uniqueness implies "at most one".

Assertion

Ref	Expression
eumo	|- (E!xph -> E*xph)

Proof of Theorem eumo

Step	Hyp	Ref	Expression
1		eu5 1035	. 2 |- (E!xph <-> (E.xph /\ E*xph))
2	1	pm3.27bd 263	1 |- (E!xph -> E*xph)

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

This theorem is referenced by:  eumoi 1038  euimmo 1045  eupick 1055  2eumo 1062  2eu2 1068  2eu5 1071  moeq3 1432  reuxfr 1580  euabex 1869  dffun7 2688  zfrep6 2744  fnopabg 2745  fnoprab 3038

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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