Theorem 2false 719

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		pm5.21 677	. 2 |- ((-. ph /\ -. ps) -> (ph <-> ps))
4	1, 2, 3	mp2an 697	1 |- (ph <-> ps)

Syntax hints:  -. wn 2   <-> wb 146

This theorem is referenced by:  iun0 2604  0iun 2605  xp0r 3239  dm0 3323  dmsn0 3324  dmsnsn0 3325  cnv0 3446  co02 3508  nn0ltp1let 6127  nn0subt 6161  zltp1let 6181

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

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