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 φBC
Assertion eqnetrrid φAC

Proof

Step Hyp Ref Expression
1 eqnetrrid.1 B=A
2 eqnetrrid.2 φBC
3 1 a1i φB=A
4 3 2 eqnetrrd φAC