Theorem moanmo 2532

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 22	. . 3 |- ( E* x ph -> E* x ph )
2		nfmo1 2481	. . . 4 |- F/ x E* x ph
3	2	moanim 2529	. . 3 |- ( E* x ( E* x ph /\ ph ) <-> ( E* x ph -> E* x ph ) )
4	1, 3	mpbir 221	. 2 |- E* x ( E* x ph /\ ph )
5		ancom 466	. . 3 |- ( ( ph /\ E* x ph ) <-> ( E* x ph /\ ph ) )
6	5	mobii 2493	. 2 |- ( E* x ( ph /\ E* x ph ) <-> E* x ( E* x ph /\ ph ) )
7	4, 6	mpbir 221	1 |- E* x ( ph /\ E* x ph )

Syntax hints:   -> wi 4   /\ wa 384   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by:  moaneu  2533