Theorem moaneu 2263

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

Assertion

Ref	Expression
moaneu	|- E*x(ph /\ E!xph)

Proof of Theorem moaneu

Step	Hyp	Ref	Expression
1		eumo 2244	. . 3 |- (E!xph -> E*xph)
2		nfeu1 2214	. . . 4 |- F/xE!xph
3	2	moanim 2260	. . 3 |- (E*x(E!xph /\ ph) <-> (E!xph -> E*xph))
4	1, 3	mpbir 200	. 2 |- E*x(E!xph /\ ph)
5		ancom 437	. . 3 |- ((ph /\ E!xph) <-> (E!xph /\ ph))
6	5	mobii 2240	. 2 |- (E*x(ph /\ E!xph) <-> E*x(E!xph /\ ph))
7	4, 6	mpbir 200	1 |- E*x(ph /\ E!xph)

Syntax hints:   -> wi 4   /\ wa 358  E!weu 2204  E*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by: (None)