Theorem syl6com

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005)

	Ref	Expression
Hypotheses	syl6com.1	|- ( ph -> ( ps -> ch ) )
	syl6com.2	|- ( ch -> th )
Assertion	syl6com	|- ( ps -> ( ph -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl6com.1	|- ( ph -> ( ps -> ch ) )
2		syl6com.2	|- ( ch -> th )
3	1 2	syl6	|- ( ph -> ( ps -> th ) )
4	3	com12	|- ( ps -> ( ph -> th ) )