Theorem 2eu2ex 1847

Description: Double existential uniqueness.

Assertion

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

Proof of Theorem 2eu2ex

Step	Hyp	Ref	Expression
1		euex 1788	. 2 |- (E!xE!yph -> E.xE!yph)
2		euex 1788	. . 3 |- (E!yph -> E.yph)
3	2	eximi 1387	. 2 |- (E.xE!yph -> E.xE.yph)
4	1, 3	syl 12	1 |- (E!xE!yph -> E.xE.yph)

Syntax hints:   -> wi 3  E.wex 1326  E!weu 1771

This theorem is referenced by:  2eu1 1853

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

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