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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 4244 | . 2 ⊢ ((⊥‘𝐵) ∩ (𝐵 ∨ℋ 𝐴)) ⊆ (⊥‘𝐵) | |
3 | 1, 2 | eqsstri 4029 | 1 ⊢ 𝑅 ⊆ (⊥‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∩ cin 3961 ⊆ wss 3962 ‘cfv 6562 (class class class)co 7430 ⊥cort 30958 ∨ℋ chj 30961 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-v 3479 df-in 3969 df-ss 3979 |
This theorem is referenced by: 3oalem5 31694 |
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