Theorem 2eumo 1846

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 1816	. 2 |- (A.x(E!yph -> E*yph) -> (E!xE*yph -> E*xE!yph))
2		eumo 1807	. 2 |- (E!yph -> E*yph)
3	1, 2	mpg 1332	1 |- (E!xE*yph -> E*xE!yph)

Syntax hints:   -> wi 3  E!weu 1771  E*wmo 1772

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-eu 1775  df-mo 1776

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