Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
||
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 30755 | . 2 ⊢ pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} | |
2 | 1 | ssrab3 3688 | 1 ⊢ pred(𝑋, 𝐴, 𝑅) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3574 class class class wbr 4653 predc-bnj14 30754 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-in 3581 df-ss 3588 df-bnj14 30755 |
This theorem is referenced by: bnj229 30954 bnj517 30955 bnj1128 31058 bnj1145 31061 bnj1137 31063 bnj1408 31104 bnj1417 31109 bnj1523 31139 |
Copyright terms: Public domain | W3C validator |