Theorem mosub 1894

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 1892	. 2 |- E*y y = A
2		mosub.1	. . 3 |- E*xph
3	2	ax-gen 955	. 2 |- A.yE*xph
4		moexexv 1416	. 2 |- ((E*y y = A /\ A.yE*xph) -> E*xE.y(y = A /\ ph))
5	1, 3, 4	mp2an 694	1 |- E*xE.y(y = A /\ ph)

Syntax hints:   /\ wa 223  A.wal 950  E.wex 956   = wceq 1099  E*wmo 1358

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955  ax-8 1101  ax-9 1102  ax-10 1103  ax-12 1104  ax-11 1180  ax-17 1190  ax-16 1194  ax-11o 1202  ax-ext 1436

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 957  df-sb 1155  df-eu 1359  df-mo 1360  df-clab 1441  df-cleq 1446  df-clel 1449  df-v 1787

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