Theorem const 852

Description: Contraposition when the antecedent is a negated stable proposition. See comment of condc 853. (Contributed by BJ, 18-Nov-2023.) (Proof shortened by BJ, 11-Nov-2024.)

Assertion

Ref	Expression
const	|- (STAB ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )

Proof of Theorem const

Step	Hyp	Ref	Expression
1		con2 643	. 2 |- ( ( -. ph -> -. ps ) -> ( ps -> -. -. ph ) )
2		df-stab 831	. . 3 |- (STAB ph <-> ( -. -. ph -> ph ) )
3	2	biimpi 120	. 2 |- (STAB ph -> ( -. -. ph -> ph ) )
4	1, 3	syl9r 73	1 |- (STAB ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4  STAB wstab 830

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117  df-stab 831

This theorem is referenced by:  condc  853