Theorem negel

Description: An inference for negation elimination. (Contributed by Giovanni Mascellani, 24-May-2019)

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

Proof

Step	Hyp	Ref	Expression
1		negel.1	|- ( ps -> ch )
2		negel.2	|- ( ph -> -. ch )
3	1	adantl	|- ( ( ph /\ ps ) -> ch )
4	2	adantr	|- ( ( ph /\ ps ) -> -. ch )
5	3 4	pm2.21fal	|- ( ( ph /\ ps ) -> F. )