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Mirrors > Home > ILE Home > Th. List > cbvrmo | Unicode version |
Description: Change the bound variable of restricted "at most one" using implicit substitution. (Contributed by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
cbvral.1 |
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cbvral.2 |
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cbvral.3 |
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Ref | Expression |
---|---|
cbvrmo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvral.1 |
. . . 4
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2 | cbvral.2 |
. . . 4
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3 | cbvral.3 |
. . . 4
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4 | 1, 2, 3 | cbvrex 2587 |
. . 3
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5 | 1, 2, 3 | cbvreu 2588 |
. . 3
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6 | 4, 5 | imbi12i 237 |
. 2
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7 | rmo5 2582 |
. 2
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8 | rmo5 2582 |
. 2
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9 | 6, 7, 8 | 3bitr4i 210 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-reu 2366 df-rmo 2367 |
This theorem is referenced by: cbvrmov 2593 cbvdisj 3832 |
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