Theorem moanmo 1831

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 73	. . 3 |- (E*xph -> E*xph)
2		hbmo1 1802	. . . 4 |- (E*xph -> A.xE*xph)
3	2	moanim 1826	. . 3 |- (E*x(E*xph /\ ph) <-> (E*xph -> E*xph))
4	1, 3	mpbir 207	. 2 |- E*x(E*xph /\ ph)
5		ancom 482	. . 3 |- ((ph /\ E*xph) <-> (E*xph /\ ph))
6	5	mobii 1801	. 2 |- (E*x(ph /\ E*xph) <-> E*x(E*xph /\ ph))
7	4, 6	mpbir 207	1 |- E*x(ph /\ E*xph)

Syntax hints:   -> wi 3   /\ wa 240  E*wmo 1772

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-eu 1775  df-mo 1776

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