Description: Two classes are not elements of each other simultaneously. This is just a rewriting of en2lp and serves as an example in the context of Godel codes, see elnanelprv . (Contributed by AV, 5-Nov-2023) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | elnanel | |- ( A e. B -/\ B e. A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en2lp | |- -. ( A e. B /\ B e. A ) |
|
2 | df-nan | |- ( ( A e. B -/\ B e. A ) <-> -. ( A e. B /\ B e. A ) ) |
|
3 | 1 2 | mpbir | |- ( A e. B -/\ B e. A ) |