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Metamath Proof Explorer

Theorem pm2.21ddne

Description: A contradiction implies anything. Equality/inequality deduction form. (Contributed by David Moews, 28-Feb-2017)

Ref Expression
Hypotheses pm2.21ddne.1 
|- ( ph -> A = B )
pm2.21ddne.2 
|- ( ph -> A =/= B )
Assertion pm2.21ddne 
|- ( ph -> ps )

Proof

Step Hyp Ref Expression
1 pm2.21ddne.1 
 |-  ( ph -> A = B )
2 pm2.21ddne.2 
 |-  ( ph -> A =/= B )
3 2 neneqd 
 |-  ( ph -> -. A = B )
4 1 3 pm2.21dd 
 |-  ( ph -> ps )