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Theorem elnelne1 2804
Description: Two classes are different if they don't contain the same element. (Contributed by AV, 28-Jan-2020.)
Assertion
Ref Expression
elnelne1

Proof of Theorem elnelne1
StepHypRef Expression
1 df-nel 2655 . 2
2 nelne1 2786 . 2
31, 2sylan2b 475 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  e.wcel 1818  =/=wne 2652  e/wnel 2653
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452  df-ne 2654  df-nel 2655
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