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  1244  dftru2  1250  bitru  1254  vjust  2552  pwv  3570  int0  3620  0iin  3706  snnex  4147  ruv  4228  fo1st  5726  fo2nd  5727  eqer  6074  ener  6195  bdth  9220