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| Mirrors > Home > MPE Home > Th. List > abanssr | Structured version Visualization version GIF version | ||
| Description: A class abstraction with a conjunction is a subset of the class abstraction with the right conjunct only. (Contributed by AV, 7-Aug-2024.) (Proof shortened by SN, 22-Aug-2024.) |
| Ref | Expression |
|---|---|
| abanssr | ⊢ {𝑓 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑓 ∣ 𝜓} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpr 484 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
| 2 | 1 | ss2abi 4067 | 1 ⊢ {𝑓 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑓 ∣ 𝜓} |
| Colors of variables: wff setvar class |
| Syntax hints: ∧ wa 395 {cab 2714 ⊆ wss 3951 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-sb 2065 df-clab 2715 df-ss 3968 |
| This theorem is referenced by: hashf1lem1 14494 |
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