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Mirrors > Home > ILE Home > Th. List > sb4or | Unicode version |
Description: One direction of a simplified definition of substitution when variables are distinct. Similar to sb4 1805 but stronger in intuitionistic logic. (Contributed by Jim Kingdon, 2-Feb-2018.) |
Ref | Expression |
---|---|
sb4or |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equs5or 1803 |
. 2
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2 | nfe1 1473 |
. . . . . 6
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3 | nfa1 1522 |
. . . . . 6
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4 | 2, 3 | nfim 1552 |
. . . . 5
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5 | 4 | nfri 1500 |
. . . 4
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6 | sb1 1740 |
. . . . 5
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7 | 6 | imim1i 60 |
. . . 4
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8 | 5, 7 | alrimih 1446 |
. . 3
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9 | 8 | orim2i 751 |
. 2
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10 | 1, 9 | ax-mp 5 |
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-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: sb4bor 1808 nfsb2or 1810 |
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