Theorem moanmo 1431

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 1406	. . . 4 |- (E*xph -> A.xE*xph)
3	2	moanim 1427	. . 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 1405	. 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 1381

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383

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