Theorem 2eumo 1485

Description: Double quantification with existential uniqueness and "at most one."

Assertion

Ref	Expression
2eumo	|- (E!xE*yph -> E*xE!yph)

Proof of Theorem 2eumo

Step	Hyp	Ref	Expression
1		euimmo 1462	. 2 |- (A.x(E!yph -> E*yph) -> (E!xE*yph -> E*xE!yph))
2		eumo 1453	. 2 |- (E!yph -> E*yph)
3	1, 2	mpg 1027	1 |- (E!xE*yph -> E*xE!yph)

Syntax hints:   -> wi 3  E!weu 1422  E*wmo 1423

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1003  ax-gen 1004  ax-8 1005  ax-10 1007  ax-11 1008  ax-12 1009  ax-17 1012  ax-4 1014  ax-5o 1016  ax-6o 1019  ax-9o 1164  ax-10o 1182  ax-16 1252  ax-11o 1260

This theorem depends on definitions:  df-bi 154  df-or 231  df-an 232  df-ex 1022  df-sb 1214  df-eu 1424  df-mo 1425

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