Theorem bibi1i 305

Description: Inference adding a biconditional to the right in an equivalence. (Contributed by NM, 5-Aug-1993.)

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 191	. 2 |- ((ph <-> ch) <-> (ch <-> ph))
2		bibi.a	. . 3 |- (ph <-> ps)
3	2	bibi2i 304	. 2 |- ((ch <-> ph) <-> (ch <-> ps))
4		bicom 191	. 2 |- ((ch <-> ps) <-> (ps <-> ch))
5	1, 3, 4	3bitri 262	1 |- ((ph <-> ch) <-> (ps <-> ch))

Syntax hints:   <-> wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  bibi12i  306  biluk  899  xorass  1308  hadbi  1387  sbrbis  2073  ssequn1  3434  axssetprim  4093