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Metamath Proof Explorer

Theorem eqnetrrid

Description: A chained equality inference for inequality. (Contributed by NM, 6-Jun-2012) (Proof shortened by Wolf Lammen, 19-Nov-2019)

Ref Expression
Hypotheses eqnetrrid.1 
|- B = A
eqnetrrid.2 
|- ( ph -> B =/= C )
Assertion eqnetrrid 
|- ( ph -> A =/= C )

Proof

Step Hyp Ref Expression
1 eqnetrrid.1 
 |-  B = A
2 eqnetrrid.2 
 |-  ( ph -> B =/= C )
3 1 a1i 
 |-  ( ph -> B = A )
4 3 2 eqnetrrd 
 |-  ( ph -> A =/= C )