Theorem 3imtr3g 204

Description: More general version of 3imtr3i 200. Useful for converting definitions in a formula. (Contributed by NM, 20-May-1996.) (Proof shortened by Wolf Lammen, 20-Dec-2013.)

Hypotheses

Ref	Expression
3imtr3g.1	|- ( ph -> ( ps -> ch ) )
3imtr3g.2	|- ( ps <-> th )
3imtr3g.3	|- ( ch <-> ta )

Assertion

Ref	Expression
3imtr3g	|- ( ph -> ( th -> ta ) )

Proof of Theorem 3imtr3g

Step	Hyp	Ref	Expression
1		3imtr3g.2	. . 3 |- ( ps <-> th )
2		3imtr3g.1	. . 3 |- ( ph -> ( ps -> ch ) )
3	1, 2	biimtrrid 153	. 2 |- ( ph -> ( th -> ch ) )
4		3imtr3g.3	. 2 |- ( ch <-> ta )
5	3, 4	imbitrdi 161	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:  dvelimfALT2  1828  dvelimf  2027  dveeq1  2031  sspwb  4237  ssopab2b  4297  wetrep  4381  imadif  5318  ssoprab2b  5957  iinerm  6637  uzind  9400  bezoutlembi  12048  subrgdvds  13608