Theorem pm2.65d

Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 26-May-2013)

	Ref	Expression
Hypotheses	pm2.65d.1	|- ( ph -> ( ps -> ch ) )
	pm2.65d.2	|- ( ph -> ( ps -> -. ch ) )
Assertion	pm2.65d	|- ( ph -> -. ps )

Proof

Step	Hyp	Ref	Expression
1		pm2.65d.1	|- ( ph -> ( ps -> ch ) )
2		pm2.65d.2	|- ( ph -> ( ps -> -. ch ) )
3	2 1	nsyld	|- ( ph -> ( ps -> -. ps ) )
4	3	pm2.01d	|- ( ph -> -. ps )