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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj213 | 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 |
---|---|
bnj213 | ⊢ pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bnj14 30008 | . 2 ⊢ pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} | |
2 | 1 | bnj21 30037 | 1 ⊢ pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3540 class class class wbr 4583 predc-bnj14 30007 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rab 2905 df-in 3547 df-ss 3554 df-bnj14 30008 |
This theorem is referenced by: bnj229 30208 bnj517 30209 bnj1128 30312 bnj1145 30315 bnj1137 30317 bnj1408 30358 bnj1417 30363 bnj1523 30393 |
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