Theorem pm14.12 16385

Description: Theorem *14.12 in [WhiteheadRussell] p. 184.

Assertion

Ref	Expression
pm14.12	|- (E!xph -> A.xA.y((ph /\ [y / x]ph) -> x = y))

Distinct variable groups:   ph,y   x,y

Proof of Theorem pm14.12

Step	Hyp	Ref	Expression
1		eumo 1807	. 2 |- (E!xph -> E*xph)
2		ax-17 1317	. . 3 |- (ph -> A.yph)
3	2	mo3 1797	. 2 |- (E*xph <-> A.xA.y((ph /\ [y / x]ph) -> x = y))
4	1, 3	sylib 215	1 |- (E!xph -> A.xA.y((ph /\ [y / x]ph) -> x = y))

Syntax hints:   -> wi 3   /\ wa 240  A.wal 1296   = wceq 1298  [wsbc 1534  E!weu 1771  E*wmo 1772

This theorem is referenced by:  pm14.24 16397

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  df-mo 1776

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