Theorem 2th 173

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 125	1 |- ( ph <-> ps )

Syntax hints:   <-> wb 104

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  trujust  1344  dftru2  1350  bitru  1354  vjust  2722  pwv  3782  int0  3832  0iin  3918  snnex  4420  ruv  4521  fo1st  6117  fo2nd  6118  eqer  6524  ener  6736  rexfiuz  10917  bdth  13548