Theorem 2false 653

Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Hypotheses

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

Assertion

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

Proof of Theorem 2false

Step	Hyp	Ref	Expression
1		2false.1	. . 3 |- -. ph
2	1	pm2.21i 611	. 2 |- ( ph -> ps )
3		2false.2	. . 3 |- -. ps
4	3	pm2.21i 611	. 2 |- ( ps -> ph )
5	2, 4	impbii 125	1 |- ( ph <-> ps )

Syntax hints:   -. wn 3   <-> wb 104

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 106  ax-ia3 107  ax-in2 581

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  bianfi  894  bifal  1303  dfnul2  3289  dfnul3  3290  rab0  3315  iun0  3792  0iun  3793  0xp  4531  cnv0  4848  co02  4957  0er  6340  bdnth  11998  bdnthALT  11999