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Mirrors > Home > ILE Home > Th. List > sb4bor | Unicode version |
Description: Simplified definition of substitution when variables are distinct, expressed via disjunction. (Contributed by Jim Kingdon, 18-Mar-2018.) |
Ref | Expression |
---|---|
sb4bor |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb4or 1711 |
. 2
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2 | sb2 1647 |
. . . . 5
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3 | df-bi 110 |
. . . . . 6
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4 | 3 | simpri 106 |
. . . . 5
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5 | 2, 4 | mpan2 401 |
. . . 4
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6 | 5 | alimi 1341 |
. . 3
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7 | 6 | orim2i 677 |
. 2
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8 | 1, 7 | ax-mp 7 |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 |
This theorem is referenced by: (None) |
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