Theorem syl5com

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 24-May-2005)

	Ref	Expression
Hypotheses	syl5com.1	|- ( ph -> ps )
	syl5com.2	|- ( ch -> ( ps -> th ) )
Assertion	syl5com	|- ( ph -> ( ch -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl5com.1	|- ( ph -> ps )
2		syl5com.2	|- ( ch -> ( ps -> th ) )
3	1	a1d	|- ( ph -> ( ch -> ps ) )
4	3 2	sylcom	|- ( ph -> ( ch -> th ) )