Theorem biantrud

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 2-Aug-1994) (Proof shortened by Wolf Lammen, 23-Oct-2013)

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

Proof

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