Theorem bnj951

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj951.1	|- ( ta -> ph )
	bnj951.2	|- ( ta -> ps )
	bnj951.3	|- ( ta -> ch )
	bnj951.4	|- ( ta -> th )
Assertion	bnj951	|- ( ta -> ( ph /\ ps /\ ch /\ th ) )

Proof

Step	Hyp	Ref	Expression
1		bnj951.1	|- ( ta -> ph )
2		bnj951.2	|- ( ta -> ps )
3		bnj951.3	|- ( ta -> ch )
4		bnj951.4	|- ( ta -> th )
5	1 2 3	3jca	|- ( ta -> ( ph /\ ps /\ ch ) )
6		df-bnj17	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )
7	5 4 6	sylanbrc	|- ( ta -> ( ph /\ ps /\ ch /\ th ) )