Theorem 2th 163

Description: Two truths are equivalent. (Contributed by NM, 18-Aug-1993.)

Hypotheses

Ref	Expression
2th.1	|- ph
2th.2	|- ps

Assertion

Ref	Expression
2th	|- ( ph <-> ps )

Proof of Theorem 2th

Step	Hyp	Ref	Expression
1		2th.2	. . 3 |- ps
2	1	a1i 9	. 2 |- ( ph -> ps )
3		2th.1	. . 3 |- ph
4	3	a1i 9	. 2 |- ( ps -> ph )
5	2, 4	impbii 117	1 |- ( ph <-> ps )

Syntax hints:   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  trujust  1245  dftru2  1251  bitru  1255  vjust  2558  pwv  3579  int0  3629  0iin  3715  snnex  4181  ruv  4274  fo1st  5784  fo2nd  5785  eqer  6138  ener  6259  bdth  9951