Theorem mosub 2981

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 2980	. 2 |- ( A. y E* x ph -> E* x E. y ( y = A /\ ph ) )
2		mosub.1	. 2 |- E* x ph
3	1, 2	mpg 1497	1 |- E* x E. y ( y = A /\ ph )

Syntax hints:   /\ wa 104   = wceq 1395   E.wex 1538   E*wmo 2078

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081  df-clab 2216  df-cleq 2222  df-clel 2225  df-v 2801

This theorem is referenced by: (None)