Theorem syl21anbrc

Description: Syllogism inference. (Contributed by Peter Mazsa, 18-Sep-2022)

	Ref	Expression
Hypotheses	syl21anbrc.1	|- ( ph -> ps )
	syl21anbrc.2	|- ( ph -> ch )
	syl21anbrc.3	|- ( ph -> th )
	syl21anbrc.4	|- ( ta <-> ( ( ps /\ ch ) /\ th ) )
Assertion	syl21anbrc	|- ( ph -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl21anbrc.1	|- ( ph -> ps )
2		syl21anbrc.2	|- ( ph -> ch )
3		syl21anbrc.3	|- ( ph -> th )
4		syl21anbrc.4	|- ( ta <-> ( ( ps /\ ch ) /\ th ) )
5	1 2 3	jca31	|- ( ph -> ( ( ps /\ ch ) /\ th ) )
6	5 4	sylibr	|- ( ph -> ta )