Theorem sylnbir

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

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

Proof

Step	Hyp	Ref	Expression
1		sylnbir.1	|- ( ps <-> ph )
2		sylnbir.2	|- ( -. ps -> ch )
3	1	bicomi	|- ( ph <-> ps )
4	3 2	sylnbi	|- ( -. ph -> ch )