Metamath Proof Explorer


Theorem neeqtrd

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

Ref Expression
Hypotheses neeqtrd.1 φAB
neeqtrd.2 φB=C
Assertion neeqtrd φAC

Proof

Step Hyp Ref Expression
1 neeqtrd.1 φAB
2 neeqtrd.2 φB=C
3 2 neeq2d φABAC
4 1 3 mpbid φAC