Theorem 2false 702

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 647	. 2 |- ( ph -> ps )
3		2false.2	. . 3 |- -. ps
4	3	pm2.21i 647	. 2 |- ( ps -> ph )
5	2, 4	impbii 126	1 |- ( ph <-> ps )

Syntax hints:   -. wn 3   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  bianfi  949  bifal  1377  dfnul2  3452  dfnul3  3453  rab0  3479  iun0  3973  0iun  3974  0xp  4743  cnv0  5073  co02  5183  0er  6626  2lgslem4  15344  bdnth  15480  bdnthALT  15481