Theorem euimmo 1418

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 1415	. 2 |- (A.x(ph -> ps) -> (E*xps -> E*xph))
2		eumo 1409	. 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 952  E!weu 1378  E*wmo 1379

This theorem is referenced by:  euim 1419  2eumo 1440  moeq3 1917  reuss2 2271

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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