Theorem sylnibr

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

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

Proof

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