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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 31961 | . 2 ⊢ pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} | |
2 | 1 | ssrab3 4059 | 1 ⊢ pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3938 class class class wbr 5068 predc-bnj14 31960 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-in 3945 df-ss 3954 df-bnj14 31961 |
This theorem is referenced by: bnj229 32158 bnj517 32159 bnj1128 32264 bnj1145 32267 bnj1137 32269 bnj1408 32310 bnj1417 32315 bnj1523 32345 |
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