Theorem euimmo 1459

Description: Uniqueness implies "at most one" through implication.

Assertion

Ref	Expression
euimmo	|- (A.x(ph -> ps) -> (E!xps -> E*xph))

Proof of Theorem euimmo

Step	Hyp	Ref	Expression
1		immo 1456	. 2 |- (A.x(ph -> ps) -> (E*xps -> E*xph))
2		eumo 1450	. 2 |- (E!xps -> E*xps)
3	1, 2	syl5 21	1 |- (A.x(ph -> ps) -> (E!xps -> E*xph))

Syntax hints:   -> wi 3  A.wal 990  E!weu 1419  E*wmo 1420

This theorem is referenced by:  euim 1460  2eumo 1482  moeq3 1967  reuss2 2327

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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