Metamath Proof Explorer


Theorem neeqtrrd

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

Ref Expression
Hypotheses neeqtrrd.1 ( 𝜑𝐴𝐵 )
neeqtrrd.2 ( 𝜑𝐶 = 𝐵 )
Assertion neeqtrrd ( 𝜑𝐴𝐶 )

Proof

Step Hyp Ref Expression
1 neeqtrrd.1 ( 𝜑𝐴𝐵 )
2 neeqtrrd.2 ( 𝜑𝐶 = 𝐵 )
3 2 eqcomd ( 𝜑𝐵 = 𝐶 )
4 1 3 neeqtrd ( 𝜑𝐴𝐶 )