Theorem mosub 2904

Description: "At most one" remains true after substitution. (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
mosub.1	|- E* x ph

Assertion

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

Distinct variable group:   x, y, A

Allowed substitution hints:   ph( x, y)

Proof of Theorem mosub

Step	Hyp	Ref	Expression
1		mosubt 2903	. 2 |- ( A. y E* x ph -> E* x E. y ( y = A /\ ph ) )
2		mosub.1	. 2 |- E* x ph
3	1, 2	mpg 1439	1 |- E* x E. y ( y = A /\ ph )

Syntax hints:   /\ wa 103   = wceq 1343   E.wex 1480   E*wmo 2015

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2728

This theorem is referenced by: (None)