Theorem bibi12i 229

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 227	. 2 |- ( ( ph <-> ch ) <-> ( ph <-> th ) )
3		bibi.a	. . 3 |- ( ph <-> ps )
4	3	bibi1i 228	. 2 |- ( ( ph <-> th ) <-> ( ps <-> th ) )
5	2, 4	bitri 184	1 |- ( ( ph <-> ch ) <-> ( ps <-> th ) )

Syntax hints:   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.7dc  956  asymref  5055  rexrnmpt  5705  uzennn  10528