Theorem 3imtr3g 203

Description: More general version of 3imtr3i 199. 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	syl5bir 152	. 2 |- ( ph -> ( th -> ch ) )
4		3imtr3g.3	. 2 |- ( ch <-> ta )
5	3, 4	syl6ib 160	1 |- ( ph -> ( th -> ta ) )

Syntax hints:   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  dvelimfALT2  1805  dvelimf  2003  dveeq1  2007  sspwb  4194  ssopab2b  4254  wetrep  4338  imadif  5268  ssoprab2b  5899  iinerm  6573  uzind  9302  bezoutlembi  11938