Theorem syl9r

Description: A nested syllogism inference with different antecedents. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypotheses	syl9r.1	|- ( ph -> ( ps -> ch ) )
	syl9r.2	|- ( th -> ( ch -> ta ) )
Assertion	syl9r	|- ( th -> ( ph -> ( ps -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		syl9r.1	|- ( ph -> ( ps -> ch ) )
2		syl9r.2	|- ( th -> ( ch -> ta ) )
3	1 2	syl9	|- ( ph -> ( th -> ( ps -> ta ) ) )
4	3	com12	|- ( th -> ( ph -> ( ps -> ta ) ) )