Theorem 2th 174

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 126	1 |- ( ph <-> ps )

Syntax hints:   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  trujust  1400  dftru2  1406  bitru  1410  vjust  2804  pwv  3897  int0  3947  0iin  4034  snnex  4551  ruv  4654  fo1st  6329  fo2nd  6330  eqer  6777  ener  6996  rexfiuz  11629  bdth  16547