Theorem alexn 1044

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 1038	. . 3 |- (E.y -. ph <-> -. A.yph)
2	1	albii 999	. 2 |- (A.xE.y -. ph <-> A.x -. A.yph)
3		alnex 1033	. 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 954  E.wex 980

This theorem is referenced by:  nalset 2712  kmlem2 4766

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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