Theorem stabnot 828

Description: Every negated formula is stable. (Contributed by David A. Wheeler, 13-Aug-2018.)

Assertion

Ref	Expression
stabnot	|- STAB -. ph

Proof of Theorem stabnot

Step	Hyp	Ref	Expression
1		notnotnot 629	. . 3 |- ( -. -. -. ph <-> -. ph )
2	1	biimpi 119	. 2 |- ( -. -. -. ph -> -. ph )
3		df-stab 826	. 2 |- (STAB -. ph <-> ( -. -. -. ph -> -. ph ) )
4	2, 3	mpbir 145	1 |- STAB -. ph

Syntax hints:   -. wn 3   -> wi 4  STAB wstab 825

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610

This theorem depends on definitions:  df-bi 116  df-stab 826

This theorem is referenced by:  dcnn  843  cnstab  8564