Theorem alexn 726

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 721	. . 3 |- (E.y -. ph <-> -. A.yph)
2	1	bial 695	. 2 |- (A.xE.y -. ph <-> A.x -. A.yph)
3		alnex 716	. 2 |- (A.x -. A.yph <-> -. E.xA.yph)
4	2, 3	bitr 151	1 |- (A.xE.y -. ph <-> -. E.xA.yph)

Syntax hints:  -. wn 1   <-> wb 127  A.wal 672  E.wex 678

This theorem is referenced by:  nalset 1482  kmlem2 3581

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

metamath.org