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Mirrors > Home > ILE Home > Th. List > tfr1onlemssrecs | Unicode version |
Description: Lemma for tfr1on 6177. The union of functions acceptable for tfr1on 6177 is a subset of recs. (Contributed by Jim Kingdon, 15-Mar-2022.) |
Ref | Expression |
---|---|
tfr1onlemssrecs.1 |
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tfr1onlemssrecs.x |
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Ref | Expression |
---|---|
tfr1onlemssrecs |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfr1onlemssrecs.1 |
. . . 4
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2 | tfr1onlemssrecs.x |
. . . . . 6
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3 | ordsson 4346 |
. . . . . 6
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4 | ssrexv 3109 |
. . . . . 6
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5 | 2, 3, 4 | 3syl 17 |
. . . . 5
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6 | 5 | ss2abdv 3117 |
. . . 4
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7 | 1, 6 | syl5eqss 3093 |
. . 3
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8 | 7 | unissd 3707 |
. 2
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9 | df-recs 6132 |
. 2
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10 | 8, 9 | syl6sseqr 3096 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-in 3027 df-ss 3034 df-uni 3684 df-tr 3967 df-iord 4226 df-on 4228 df-recs 6132 |
This theorem is referenced by: tfr1onlembfn 6171 tfr1onlemubacc 6173 tfr1onlemres 6176 |
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