Theorem 2eumo 1440

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 1418	. 2 |- (A.x(E!yph -> E*yph) -> (E!xE*yph -> E*xE!yph))
2		eumo 1409	. 2 |- (E!yph -> E*yph)
3	1, 2	mpg 984	1 |- (E!xE*yph -> E*xE!yph)

Syntax hints:   -> wi 3  E!weu 1378  E*wmo 1379

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381

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