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Mirrors > Home > ILE Home > Th. List > hbequid | Unicode version |
Description: Bound-variable hypothesis
builder for ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() The proof uses only ax-8 1504 and ax-i12 1507 on top of (the FOL analogue of) modal logic KT. This shows that this can be proved without ax-i9 1530, even though Theorem equid 1701 cannot. A shorter proof using ax-i9 1530 is obtainable from equid 1701 and hbth 1463. (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 23-Mar-2014.) |
Ref | Expression |
---|---|
hbequid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12or 1508 |
. 2
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2 | ax-8 1504 |
. . . . . 6
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3 | 2 | pm2.43i 49 |
. . . . 5
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4 | 3 | alimi 1455 |
. . . 4
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5 | 4 | a1d 22 |
. . 3
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6 | ax-4 1510 |
. . . 4
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7 | 5, 6 | jaoi 716 |
. . 3
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8 | 5, 7 | jaoi 716 |
. 2
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9 | 1, 8 | 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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-gen 1449 ax-8 1504 ax-i12 1507 ax-4 1510 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: equveli 1759 |
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