Theorem bj-pm2.18st 13631

Description: Clavius law for stable formulas. See pm2.18dc 845. (Contributed by BJ, 4-Dec-2023.)

Assertion

Ref	Expression
bj-pm2.18st	|- (STAB ph -> ( ( -. ph -> ph ) -> ph ) )

Proof of Theorem bj-pm2.18st

Step	Hyp	Ref	Expression
1		df-stab 821	. 2 |- (STAB ph <-> ( -. -. ph -> ph ) )
2		bj-nnclavius 13618	. . 3 |- ( ( -. ph -> ph ) -> -. -. ph )
3	2	imim1i 60	. 2 |- ( ( -. -. ph -> ph ) -> ( ( -. ph -> ph ) -> ph ) )
4	1, 3	sylbi 120	1 |- (STAB ph -> ( ( -. ph -> ph ) -> ph ) )

Syntax hints:   -. wn 3   -> wi 4  STAB wstab 820

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116  df-stab 821

This theorem is referenced by: (None)