Theorem bicontr 33879

Description: Biimplication of its own negation is a contradiction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Assertion

Ref	Expression
bicontr	|- ( ( -. ph <-> ph ) <-> F. )

Proof of Theorem bicontr

Step	Hyp	Ref	Expression
1		biid 251	. . 3 |- ( ph <-> ph )
2		notbinot1 33878	. . 3 |- ( -. ( -. ph <-> ph ) <-> ( ph <-> ph ) )
3	1, 2	mpbir 221	. 2 |- -. ( -. ph <-> ph )
4	3	bifal 1497	1 |- ( ( -. ph <-> ph ) <-> F. )

Syntax hints:   -. wn 3   <-> wb 196   F. wfal 1488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)