Theorem moanmo 1424

Description: Nested "at most one" quantifiers.

Assertion

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

Proof of Theorem moanmo

Step	Hyp	Ref	Expression
1		id 59	. . 3 |- (E*xph -> E*xph)
2		hbmo1 1399	. . . 4 |- (E*xph -> A.xE*xph)
3	2	moanim 1420	. . 3 |- (E*x(E*xph /\ ph) <-> (E*xph -> E*xph))
4	1, 3	mpbir 190	. 2 |- E*x(E*xph /\ ph)
5		ancom 435	. . 3 |- ((ph /\ E*xph) <-> (E*xph /\ ph))
6	5	mobii 1398	. 2 |- (E*x(ph /\ E*xph) <-> E*x(E*xph /\ ph))
7	4, 6	mpbir 190	1 |- E*x(ph /\ E*xph)

Syntax hints:   -> wi 3   /\ wa 223  E*wmo 1374

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376

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