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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 3833 | . 2 ⊢ ((⊥‘𝐵) ∩ (𝐵 ∨ℋ 𝐴)) ⊆ (⊥‘𝐵) | |
3 | 1, 2 | eqsstri 3635 | 1 ⊢ 𝑅 ⊆ (⊥‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∩ cin 3573 ⊆ wss 3574 ‘cfv 5888 (class class class)co 6650 ⊥cort 27787 ∨ℋ chj 27790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 |
This theorem is referenced by: 3oalem5 28525 |
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