Theorem euim 1420

Description: Add existential uniqueness quantifiers to an implication. Note the reversed implication in the antecedent.

Assertion

Ref	Expression
euim	|- ((E.xph /\ A.x(ph -> ps)) -> (E!xps -> E!xph))

Proof of Theorem euim

Step	Hyp	Ref	Expression
1		euimmo 1419	. . 3 |- (A.x(ph -> ps) -> (E!xps -> E*xph))
2	1	adantl 388	. 2 |- ((E.xph /\ A.x(ph -> ps)) -> (E!xps -> E*xph))
3		exmoeu2 1413	. . 3 |- (E.xph -> (E*xph <-> E!xph))
4	3	adantr 389	. 2 |- ((E.xph /\ A.x(ph -> ps)) -> (E*xph <-> E!xph))
5	2, 4	sylibd 202	1 |- ((E.xph /\ A.x(ph -> ps)) -> (E!xps -> E!xph))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 953  E.wex 979  E!weu 1379  E*wmo 1380

This theorem is referenced by:  euor2 1436

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-11 966  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171  df-eu 1381  df-mo 1382

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