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Mirrors > Home > ILE Home > Th. List > mosubt | Unicode version |
Description: "At most one" remains true after substitution. (Contributed by Jim Kingdon, 18-Jan-2019.) |
Ref | Expression |
---|---|
mosubt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eueq 2712 |
. . . . . 6
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2 | isset 2561 |
. . . . . 6
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3 | 1, 2 | bitr3i 175 |
. . . . 5
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4 | nfv 1421 |
. . . . . 6
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5 | 4 | euexex 1985 |
. . . . 5
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6 | 3, 5 | sylanbr 269 |
. . . 4
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7 | 6 | expcom 109 |
. . 3
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8 | moanimv 1975 |
. . 3
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9 | 7, 8 | sylibr 137 |
. 2
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10 | simpl 102 |
. . . . 5
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11 | 10 | eximi 1491 |
. . . 4
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12 | 11 | ancri 307 |
. . 3
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13 | 12 | moimi 1965 |
. 2
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14 | 9, 13 | syl 14 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: mosub 2719 |
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