Theorem 3bitr3g 278

Description: More general version of 3bitr3i 266. 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	syl5bbr 250	. 2 |- (ph -> (th <-> ch))
4		3bitr3g.3	. 2 |- (ch <-> ta)
5	3, 4	syl6bb 252	1 |- (ph -> (th <-> ta))

Syntax hints:   -> wi 4   <-> 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:  notbid  285  cador  1391  equequ2  1686  dfsbcq2  3050  unineq  3506  iindif2  4036  isoini  5498  brcupg  5815  enprmaplem3  6079  nmembers1lem3  6271