Theorem alexn 1085

Description: A relationship between two quantifiers and negation.

Assertion

Ref	Expression
alexn	|- (A.xE.y -. ph <-> -. E.xA.yph)

Proof of Theorem alexn

Step	Hyp	Ref	Expression
1		exnal 1079	. . 3 |- (E.y -. ph <-> -. A.yph)
2	1	albii 1040	. 2 |- (A.xE.y -. ph <-> A.x -. A.yph)
3		alnex 1074	. 2 |- (A.x -. A.yph <-> -. E.xA.yph)
4	2, 3	bitri 180	1 |- (A.xE.y -. ph <-> -. E.xA.yph)

Syntax hints:  -. wn 2   <-> wb 153  A.wal 995  E.wex 1021

This theorem is referenced by:  nalset 2767  kmlem2 4828

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1004  ax-4 1014  ax-5o 1016

This theorem depends on definitions:  df-bi 154  df-an 232  df-ex 1022

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