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Mirrors > Home > ILE Home > Th. List > tfrcllemssrecs | Unicode version |
Description: Lemma for tfrcl 6269. The union of functions acceptable for tfrcl 6269 is a subset of recs. (Contributed by Jim Kingdon, 25-Mar-2022.) |
Ref | Expression |
---|---|
tfrcllemssrecs.1 |
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tfrcllemssrecs.x |
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Ref | Expression |
---|---|
tfrcllemssrecs |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrcllemssrecs.1 |
. . . 4
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2 | tfrcllemssrecs.x |
. . . . . 6
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3 | ordsson 4416 |
. . . . . 6
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4 | ssrexv 3167 |
. . . . . 6
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5 | 2, 3, 4 | 3syl 17 |
. . . . 5
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6 | 5 | ss2abdv 3175 |
. . . 4
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7 | 1, 6 | eqsstrid 3148 |
. . 3
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8 | 7 | unissd 3768 |
. 2
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9 | ffn 5280 |
. . . . . . 7
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10 | 9 | anim1i 338 |
. . . . . 6
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11 | 10 | reximi 2532 |
. . . . 5
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12 | 11 | ss2abi 3174 |
. . . 4
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13 | 12 | unissi 3767 |
. . 3
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14 | df-recs 6210 |
. . 3
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15 | 13, 14 | sseqtrri 3137 |
. 2
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16 | 8, 15 | sstrdi 3114 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-in 3082 df-ss 3089 df-uni 3745 df-tr 4035 df-iord 4296 df-on 4298 df-f 5135 df-recs 6210 |
This theorem is referenced by: tfrcllembfn 6262 tfrcllemubacc 6264 tfrcllemres 6267 |
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