Theorem moanmo 2155

Description: Nested at-most-one quantifiers. (Contributed by NM, 25-Jan-2006.)

Assertion

Ref	Expression
moanmo	|- E* x ( ph /\ E* x ph )

Proof of Theorem moanmo

Step	Hyp	Ref	Expression
1		id 19	. . 3 |- ( E* x ph -> E* x ph )
2		nfmo1 2089	. . . 4 |- F/ x E* x ph
3	2	moanim 2152	. . 3 |- ( E* x ( E* x ph /\ ph ) <-> ( E* x ph -> E* x ph ) )
4	1, 3	mpbir 146	. 2 |- E* x ( E* x ph /\ ph )
5		ancom 266	. . 3 |- ( ( ph /\ E* x ph ) <-> ( E* x ph /\ ph ) )
6	5	mobii 2114	. 2 |- ( E* x ( ph /\ E* x ph ) <-> E* x ( E* x ph /\ ph ) )
7	4, 6	mpbir 146	1 |- E* x ( ph /\ E* x ph )

Syntax hints:   -> wi 4   /\ wa 104   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

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081

This theorem is referenced by: (None)