Theorem alexn 1042

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 1036	. . 3 |- (E.y -. ph <-> -. A.yph)
2	1	albii 997	. 2 |- (A.xE.y -. ph <-> A.x -. A.yph)
3		alnex 1031	. 2 |- (A.x -. A.yph <-> -. E.xA.yph)
4	2, 3	bitr 173	1 |- (A.xE.y -. ph <-> -. E.xA.yph)

Syntax hints:  -. wn 2   <-> wb 146  A.wal 952  E.wex 978

This theorem is referenced by:  nalset 2707  kmlem2 4746

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979

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