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Mirrors > Home > HSE Home > Th. List > 3oalem4 | Structured version Visualization version GIF version |
Description: Lemma for 3OA (weak) orthoarguesian law. (Contributed by NM, 19-Oct-1999.) (New usage is discouraged.) |
Ref | Expression |
---|---|
3oalem4.3 | ⊢ 𝑅 = ((⊥‘𝐵) ∩ (𝐵 ∨ℋ 𝐴)) |
Ref | Expression |
---|---|
3oalem4 | ⊢ 𝑅 ⊆ (⊥‘𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3oalem4.3 | . 2 ⊢ 𝑅 = ((⊥‘𝐵) ∩ (𝐵 ∨ℋ 𝐴)) | |
2 | inss1 3795 | . 2 ⊢ ((⊥‘𝐵) ∩ (𝐵 ∨ℋ 𝐴)) ⊆ (⊥‘𝐵) | |
3 | 1, 2 | eqsstri 3598 | 1 ⊢ 𝑅 ⊆ (⊥‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∩ cin 3539 ⊆ wss 3540 ‘cfv 5804 (class class class)co 6549 ⊥cort 27171 ∨ℋ chj 27174 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-in 3547 df-ss 3554 |
This theorem is referenced by: 3oalem5 27909 |
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