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Mathbox for Jonathan Ben-Naim |
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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 33529 | . 2 ⊢ pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} | |
2 | 1 | ssrab3 4076 | 1 ⊢ pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3944 class class class wbr 5141 predc-bnj14 33528 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2709 df-cleq 2723 df-clel 2809 df-rab 3432 df-v 3475 df-in 3951 df-ss 3961 df-bnj14 33529 |
This theorem is referenced by: bnj229 33724 bnj517 33725 bnj1128 33830 bnj1145 33833 bnj1137 33835 bnj1408 33876 bnj1417 33881 bnj1523 33911 |
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