Theorem 3bitr4g

Description: More general version of 3bitr4i . Useful for converting definitions in a formula. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypotheses	3bitr4g.1	|- ( ph -> ( ps <-> ch ) )
	3bitr4g.2	|- ( th <-> ps )
	3bitr4g.3	|- ( ta <-> ch )
Assertion	3bitr4g	|- ( ph -> ( th <-> ta ) )

Proof

Step	Hyp	Ref	Expression
1		3bitr4g.1	|- ( ph -> ( ps <-> ch ) )
2		3bitr4g.2	|- ( th <-> ps )
3		3bitr4g.3	|- ( ta <-> ch )
4	2 1	bitrid	|- ( ph -> ( th <-> ch ) )
5	4 3	bitr4di	|- ( ph -> ( th <-> ta ) )