Theorem pm5.74rd

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 19-Mar-1997)

	Ref	Expression
Hypothesis	pm5.74rd.1	|- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )
Assertion	pm5.74rd	|- ( ph -> ( ps -> ( ch <-> th ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.74rd.1	|- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )
2		pm5.74	|- ( ( ps -> ( ch <-> th ) ) <-> ( ( ps -> ch ) <-> ( ps -> th ) ) )
3	1 2	sylibr	|- ( ph -> ( ps -> ( ch <-> th ) ) )