Theorem 3bitr3g 222

Description: More general version of 3bitr3i 210. Useful for converting definitions in a formula. (Contributed by NM, 4-Jun-1995.)

Hypotheses

Ref	Expression
3bitr3g.1	|- ( ph -> ( ps <-> ch ) )
3bitr3g.2	|- ( ps <-> th )
3bitr3g.3	|- ( ch <-> ta )

Assertion

Ref	Expression
3bitr3g	|- ( ph -> ( th <-> ta ) )

Proof of Theorem 3bitr3g

Step	Hyp	Ref	Expression
1		3bitr3g.2	. . 3 |- ( ps <-> th )
2		3bitr3g.1	. . 3 |- ( ph -> ( ps <-> ch ) )
3	1, 2	bitr3id 194	. 2 |- ( ph -> ( th <-> ch ) )
4		3bitr3g.3	. 2 |- ( ch <-> ta )
5	3, 4	bitrdi 196	1 |- ( ph -> ( th <-> ta ) )

Syntax hints:   -> wi 4   <-> 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:  con2bidc  877  sbal1yz  2029  sbal1  2030  dfsbcq2  3001  iindif2m  3995  opeqex  4294  rabxfrd  4516  eqbrrdv  4772  eqbrrdiv  4773  opelco2g  4846  opelcnvg  4858  ralrnmpt  5722  rexrnmpt  5723  fliftcnv  5864  eusvobj2  5930  f1od2  6321  ottposg  6341  ercnv  6641  exmidpw  7005  djuf1olem  7155  fzen  10165  fihasheq0  10938  divalgb  12236  isprm3  12440  eldvap  15154