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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 4175 | . 2 ⊢ (𝐵 ∩ 𝐶) ⊆ 𝐵 | |
3 | 1, 2 | eqsstri 3966 | 1 ⊢ 𝐴 ⊆ 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 ∩ cin 3897 ⊆ wss 3898 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3443 df-in 3905 df-ss 3915 |
This theorem is referenced by: bnj1253 33296 bnj1286 33298 bnj1280 33299 bnj1296 33300 |
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