Theorem bibi12i 462

Description: The equivalence of two equivalences.

Hypotheses

Ref	Expression
bibi12.1	|- (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 460	. 2 |- ((ph <-> ch) <-> (ph <-> th))
3		bibi12.1	. . 3 |- (ph <-> ps)
4	3	bibi1i 461	. 2 |- ((ph <-> th) <-> (ps <-> th))
5	2, 4	bitr 151	1 |- ((ph <-> ch) <-> (ps <-> th))

Syntax hints:   <-> wb 127

This theorem is referenced by:  pm5.32 488  biluk 512  cleq2ab 1179  dmcosseq 2572  fv2 2828  zfcndrep 3760

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

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org