Theorem bitrd

Description: Deduction form of bitri . (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 14-Apr-2013)

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

Proof

Step	Hyp	Ref	Expression
1		bitrd.1	|- ( ph -> ( ps <-> ch ) )
2		bitrd.2	|- ( ph -> ( ch <-> th ) )
3	1	pm5.74i	|- ( ( ph -> ps ) <-> ( ph -> ch ) )
4	2	pm5.74i	|- ( ( ph -> ch ) <-> ( ph -> th ) )
5	3 4	bitri	|- ( ( ph -> ps ) <-> ( ph -> th ) )
6	5	pm5.74ri	|- ( ph -> ( ps <-> th ) )