Theorem mosub 2433

Description: "At most one" remains true after substitution.

Hypothesis

Ref	Expression
mosub.1	|- E*xph

Assertion

Ref	Expression
mosub	|- E*xE.y(y = A /\ ph)

Distinct variable group:   x,y,A

Proof of Theorem mosub

Step	Hyp	Ref	Expression
1		moeq 2431	. 2 |- E*y y = A
2		mosub.1	. . 3 |- E*xph
3	2	ax-gen 1305	. 2 |- A.yE*xph
4		moexexv 1842	. 2 |- ((E*y y = A /\ A.yE*xph) -> E*xE.y(y = A /\ ph))
5	1, 3, 4	mp2an 761	1 |- E*xE.y(y = A /\ ph)

Syntax hints:   /\ wa 240  A.wal 1296   = wceq 1298  E.wex 1326  E*wmo 1772

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  ax-ext 1865

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  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294

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