Theorem bibi12i 609

Description: The equivalence of two equivalences.

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 607	. 2 |- ((ph <-> ch) <-> (ph <-> th))
3		bibi.a	. . 3 |- (ph <-> ps)
4	3	bibi1i 608	. 2 |- ((ph <-> th) <-> (ps <-> th))
5	2, 4	bitr 173	1 |- ((ph <-> ch) <-> (ps <-> th))

Syntax hints:   <-> wb 146

This theorem is referenced by:  pm5.32 643  pm5.7 745  eq2ab 1571  dmcosseq 3361  asymref 3435  fv2 3715  zfcndrep 4949  mdsldmd1 10214

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain