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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 4237 | . 2 ⊢ ((⊥‘𝐵) ∩ (𝐵 ∨ℋ 𝐴)) ⊆ (⊥‘𝐵) | |
| 3 | 1, 2 | eqsstri 4030 | 1 ⊢ 𝑅 ⊆ (⊥‘𝐵) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∩ cin 3950 ⊆ wss 3951 ‘cfv 6561 (class class class)co 7431 ⊥cort 30949 ∨ℋ chj 30952 |
| 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 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-in 3958 df-ss 3968 |
| This theorem is referenced by: 3oalem5 31685 |
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