Theorem 2eumo 1482

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 1459	. 2 |- (A.x(E!yph -> E*yph) -> (E!xE*yph -> E*xE!yph))
2		eumo 1450	. 2 |- (E!yph -> E*yph)
3	1, 2	mpg 1022	1 |- (E!xE*yph -> E*xE!yph)

Syntax hints:   -> wi 3  E!weu 1419  E*wmo 1420

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-11 1003  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-eu 1421  df-mo 1422

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