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Mirrors > Home > NFE Home > Th. List > pssne | GIF version |
Description: Two classes in a proper subclass relationship are not equal. (Contributed by NM, 16-Feb-2015.) |
Ref | Expression |
---|---|
pssne | ⊢ (A ⊊ B → A ≠ B) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pss 3261 | . 2 ⊢ (A ⊊ B ↔ (A ⊆ B ∧ A ≠ B)) | |
2 | 1 | simprbi 450 | 1 ⊢ (A ⊊ B → A ≠ B) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ≠ wne 2516 ⊆ wss 3257 ⊊ wpss 3258 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 df-pss 3261 |
This theorem is referenced by: pssned 3367 |
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