Theorem moanmo 2113

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 2048	. . . 4 |- F/ x E* x ph
3	2	moanim 2110	. . 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 2073	. 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 2037

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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-eu 2039  df-mo 2040

This theorem is referenced by: (None)