Theorem mosub 1913

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 1911	. 2 |- E*y y = A
2		mosub.1	. . 3 |- E*xph
3	2	ax-gen 960	. 2 |- A.yE*xph
4		moexexv 1432	. 2 |- ((E*y y = A /\ A.yE*xph) -> E*xE.y(y = A /\ ph))
5	1, 3, 4	mp2an 695	1 |- E*xE.y(y = A /\ ph)

Syntax hints:   /\ wa 223  A.wal 951   = wceq 953  E.wex 977  E*wmo 1374

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  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803

Copyright terms: Public domain