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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1292 | Structured version Visualization version GIF version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1292.1 | ⊢ 𝐴 = (𝐵 ∩ 𝐶) |
Ref | Expression |
---|---|
bnj1292 | ⊢ 𝐴 ⊆ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1292.1 | . 2 ⊢ 𝐴 = (𝐵 ∩ 𝐶) | |
2 | inss1 4125 | . 2 ⊢ (𝐵 ∩ 𝐶) ⊆ 𝐵 | |
3 | 1, 2 | eqsstri 3922 | 1 ⊢ 𝐴 ⊆ 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1522 ∩ cin 3858 ⊆ wss 3859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-8 2083 ax-9 2091 ax-10 2112 ax-11 2126 ax-12 2141 ax-ext 2769 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-tru 1525 df-ex 1762 df-nf 1766 df-sb 2043 df-clab 2776 df-cleq 2788 df-clel 2863 df-nfc 2935 df-v 3439 df-in 3866 df-ss 3874 |
This theorem is referenced by: bnj1253 31903 bnj1286 31905 bnj1280 31906 bnj1296 31907 |
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