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Theorem neeqtri 3004
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtr.1 𝐴𝐵
neeqtr.2 𝐵 = 𝐶
Assertion
Ref Expression
neeqtri 𝐴𝐶

Proof of Theorem neeqtri
StepHypRef Expression
1 neeqtr.1 . 2 𝐴𝐵
2 neeqtr.2 . . 3 𝐵 = 𝐶
32neeq2i 2997 . 2 (𝐴𝐵𝐴𝐶)
41, 3mpbi 220 1 𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1632  wne 2932
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-cleq 2753  df-ne 2933
This theorem is referenced by:  neeqtrri  3005
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