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Mirrors > Home > NFE Home > Th. List > dfss | GIF version |
Description: Variant of subclass definition df-ss 3259. (Contributed by NM, 3-Sep-2004.) |
Ref | Expression |
---|---|
dfss | ⊢ (A ⊆ B ↔ A = (A ∩ B)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ss 3259 | . 2 ⊢ (A ⊆ B ↔ (A ∩ B) = A) | |
2 | eqcom 2355 | . 2 ⊢ ((A ∩ B) = A ↔ A = (A ∩ B)) | |
3 | 1, 2 | bitri 240 | 1 ⊢ (A ⊆ B ↔ A = (A ∩ B)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 = wceq 1642 ∩ cin 3208 ⊆ wss 3257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-cleq 2346 df-ss 3259 |
This theorem is referenced by: dfss2 3262 iinrab2 4029 funimass1 5169 |
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