Theorem 2eu2ex 1436

Description: Double existential uniqueness.

Assertion

Ref	Expression
2eu2ex	|- (E!xE!yph -> E.xE.yph)

Proof of Theorem 2eu2ex

Step	Hyp	Ref	Expression
1		euex 1387	. 2 |- (E!xE!yph -> E.xE!yph)
2		euex 1387	. . 3 |- (E!yph -> E.yph)
3	2	19.22i 1036	. 2 |- (E.xE!yph -> E.xE.yph)
4	1, 3	syl 10	1 |- (E!xE!yph -> E.xE.yph)

Syntax hints:   -> wi 3  E.wex 977  E!weu 1373

This theorem is referenced by:  2eu1 1442

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375

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