Theorem moaneu 1428

Description: Nested "at most one" and uniqueness quantifiers.

Assertion

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

Proof of Theorem moaneu

Step	Hyp	Ref	Expression
1		eumo 1409	. . 3 |- (E!xph -> E*xph)
2		hbeu1 1386	. . . 4 |- (E!xph -> A.xE!xph)
3	2	moanim 1425	. . 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 1403	. 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!weu 1378  E*wmo 1379

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381

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