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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1293 | 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 |
---|---|
bnj1293.1 | ⊢ 𝐴 = (𝐵 ∩ 𝐶) |
Ref | Expression |
---|---|
bnj1293 | ⊢ 𝐴 ⊆ 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1293.1 | . 2 ⊢ 𝐴 = (𝐵 ∩ 𝐶) | |
2 | inss2 4245 | . 2 ⊢ (𝐵 ∩ 𝐶) ⊆ 𝐶 | |
3 | 1, 2 | eqsstri 4029 | 1 ⊢ 𝐴 ⊆ 𝐶 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∩ cin 3961 ⊆ wss 3962 |
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-rab 3433 df-v 3479 df-in 3969 df-ss 3979 |
This theorem is referenced by: bnj1253 35009 bnj1286 35011 bnj1280 35012 bnj1296 35013 |
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