Theorem 2false 717

Description: Two falsehoods are equivalent.

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	. 2 |- -. ph
2		2false.2	. 2 |- -. ps
3		pm5.21 675	. 2 |- ((-. ph /\ -. ps) -> (ph <-> ps))
4	1, 2, 3	mp2an 695	1 |- (ph <-> ps)

Syntax hints:  -. wn 2   <-> wb 146

This theorem is referenced by:  iun0 2594  0iun 2595  xp0r 3229  dm0 3312  dmsn0 3313  dmsnsn0 3314  cnv0 3432  co02 3494  nn0ltp1let 6074  nn0subt 6108  zltp1let 6128

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain