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Metamath Proof Explorer

Theorem pm4.81

Description: A formula is equivalent to its negation implying it. Theorem *4.81 of WhiteheadRussell p. 122. Note that the second step, using pm2.24 , could also use ax-1 . (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm4.81 
|- ( ( -. ph -> ph ) <-> ph )

Proof

Step Hyp Ref Expression
1 pm2.18 
 |-  ( ( -. ph -> ph ) -> ph )
2 pm2.24 
 |-  ( ph -> ( -. ph -> ph ) )
3 1 2 impbii 
 |-  ( ( -. ph -> ph ) <-> ph )