Theorem sylnib

Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013)

	Ref	Expression
Hypotheses	sylnib.1	|- ( ph -> -. ps )
	sylnib.2	|- ( ps <-> ch )
Assertion	sylnib	|- ( ph -> -. ch )

Proof

Step	Hyp	Ref	Expression
1		sylnib.1	|- ( ph -> -. ps )
2		sylnib.2	|- ( ps <-> ch )
3	2	biimpri	|- ( ch -> ps )
4	1 3	nsyl	|- ( ph -> -. ch )