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Theorem bdne 11401
Description: Inequality of two setvars is a bounded formula. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdne BOUNDED 𝑥𝑦

Proof of Theorem bdne
StepHypRef Expression
1 ax-bdeq 11368 . . 3 BOUNDED 𝑥 = 𝑦
21ax-bdn 11365 . 2 BOUNDED ¬ 𝑥 = 𝑦
3 df-ne 2256 . 2 (𝑥𝑦 ↔ ¬ 𝑥 = 𝑦)
42, 3bd0r 11373 1 BOUNDED 𝑥𝑦
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wne 2255  BOUNDED wbd 11360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11361  ax-bdn 11365  ax-bdeq 11368
This theorem depends on definitions:  df-bi 115  df-ne 2256
This theorem is referenced by: (None)
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