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Metamath Proof Explorer

Theorem bifal

Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015)

Ref Expression
Hypothesis bifal.1 
|- -. ph
Assertion bifal 
|- ( ph <-> F. )

Proof

Step Hyp Ref Expression
1 bifal.1 
 |-  -. ph
2 fal 
 |-  -. F.
3 1 2 2false 
 |-  ( ph <-> F. )