Theorem bj-nnclavius 13772

Description: Clavius law with doubly negated consequent. (Contributed by BJ, 4-Dec-2023.)

Assertion

Ref	Expression
bj-nnclavius	|- ( ( -. ph -> ph ) -> -. -. ph )

Proof of Theorem bj-nnclavius

Step	Hyp	Ref	Expression
1		con3 637	. 2 |- ( ( -. ph -> ph ) -> ( -. ph -> -. -. ph ) )
2	1	pm2.01d 613	1 |- ( ( -. ph -> ph ) -> -. -. ph )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 609  ax-in2 610

This theorem is referenced by:  bj-pm2.18st  13785