Theorem 3imtr3g 202

Description: More general version of 3imtr3i 198. 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 151	. 2 |- ( ph -> ( th -> ch ) )
4		3imtr3g.3	. 2 |- ( ch <-> ta )
5	3, 4	syl6ib 159	1 |- ( ph -> ( th -> ta ) )

Syntax hints:   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  dvelimfALT2  1738  dvelimf  1932  dveeq1  1936  sspwb  3971  ssopab2b  4031  wetrep  4115  imadif  4999  ssoprab2b  5582  iinerm  6201  uzind  8458  bezoutlembi  10394