Theorem bibi1i 609

Description: Inference adding a biconditional to the right in an equivalence.

Hypothesis

Ref	Expression
bibi.a	|- (ph <-> ps)

Assertion

Ref	Expression
bibi1i	|- ((ph <-> ch) <-> (ps <-> ch))

Proof of Theorem bibi1i

Step	Hyp	Ref	Expression
1		bicom 520	. 2 |- ((ph <-> ch) <-> (ch <-> ph))
2		bibi.a	. . 3 |- (ph <-> ps)
3	2	bibi2i 608	. 2 |- ((ch <-> ph) <-> (ch <-> ps))
4		bicom 520	. 2 |- ((ch <-> ps) <-> (ps <-> ch))
5	1, 3, 4	3bitr 177	1 |- ((ph <-> ch) <-> (ps <-> ch))

Syntax hints:   <-> wb 146

This theorem is referenced by:  bibi12i 610  biluk 745  sbrbis 1241  aceq1 4729  aceq0 4730  axac 4745  zfcndac 4971

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