Metamath Proof Explorer


Theorem eqnetrrd

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

Ref Expression
Hypotheses eqnetrrd.1 φ A = B
eqnetrrd.2 φ A C
Assertion eqnetrrd φ B C

Proof

Step Hyp Ref Expression
1 eqnetrrd.1 φ A = B
2 eqnetrrd.2 φ A C
3 1 eqcomd φ B = A
4 3 2 eqnetrd φ B C