Theorem pm5.21nii

Description: Eliminate an antecedent implied by each side of a biconditional. (Contributed by NM, 21-May-1999)

	Ref	Expression
Hypotheses	pm5.21ni.1	|- ( ph -> ps )
	pm5.21ni.2	|- ( ch -> ps )
	pm5.21nii.3	|- ( ps -> ( ph <-> ch ) )
Assertion	pm5.21nii	|- ( ph <-> ch )

Proof

Step	Hyp	Ref	Expression
1		pm5.21ni.1	|- ( ph -> ps )
2		pm5.21ni.2	|- ( ch -> ps )
3		pm5.21nii.3	|- ( ps -> ( ph <-> ch ) )
4	1 2	pm5.21ni	|- ( -. ps -> ( ph <-> ch ) )
5	3 4	pm2.61i	|- ( ph <-> ch )