Theorem bibi12i 218

Description: The equivalence of two equivalences. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
bibi.a	|- ( ph <-> ps )
bibi12.2	|- ( ch <-> th )

Assertion

Ref	Expression
bibi12i	|- ( ( ph <-> ch ) <-> ( ps <-> th ) )

Proof of Theorem bibi12i

Step	Hyp	Ref	Expression
1		bibi12.2	. . 3 |- ( ch <-> th )
2	1	bibi2i 216	. 2 |- ( ( ph <-> ch ) <-> ( ph <-> th ) )
3		bibi.a	. . 3 |- ( ph <-> ps )
4	3	bibi1i 217	. 2 |- ( ( ph <-> th ) <-> ( ps <-> th ) )
5	2, 4	bitri 173	1 |- ( ( ph <-> ch ) <-> ( ps <-> th ) )

Syntax hints:   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm5.7dc  861  asymref  4710  rexrnmpt  5310