Theorem biantrurd

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 1-May-1995) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypothesis	biantrud.1	|- ( ph -> ps )
Assertion	biantrurd	|- ( ph -> ( ch <-> ( ps /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		biantrud.1	|- ( ph -> ps )
2		ibar	|- ( ps -> ( ch <-> ( ps /\ ch ) ) )
3	1 2	syl	|- ( ph -> ( ch <-> ( ps /\ ch ) ) )