Theorem condan

Description: Proof by contradiction. (Contributed by NM, 9-Feb-2006) (Proof shortened by Wolf Lammen, 19-Jun-2014)

	Ref	Expression
Hypotheses	condan.1	|- ( ( ph /\ -. ps ) -> ch )
	condan.2	|- ( ( ph /\ -. ps ) -> -. ch )
Assertion	condan	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		condan.1	|- ( ( ph /\ -. ps ) -> ch )
2		condan.2	|- ( ( ph /\ -. ps ) -> -. ch )
3	1 2	pm2.65da	|- ( ph -> -. -. ps )
4	3	notnotrd	|- ( ph -> ps )