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Mirrors > Home > MPE Home > Th. List > axbnd | Structured version Visualization version Unicode version |
Description: Axiom of Bundling
(intuitionistic logic axiom ax-bnd). In classical
logic, this and axi12 2440 are fairly straightforward consequences of
axc9 2151. But in intuitionistic logic, it is not easy
to add the extra
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Ref | Expression |
---|---|
axbnd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnae 2163 |
. . . . . 6
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2 | nfnae 2163 |
. . . . . 6
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3 | 1, 2 | nfan 2022 |
. . . . 5
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4 | nfnae 2163 |
. . . . . . 7
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5 | nfnae 2163 |
. . . . . . 7
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6 | 4, 5 | nfan 2022 |
. . . . . 6
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7 | axc9 2151 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | imp 435 |
. . . . . 6
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9 | 6, 8 | alrimi 1966 |
. . . . 5
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10 | 3, 9 | alrimi 1966 |
. . . 4
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11 | 10 | ex 440 |
. . 3
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12 | 11 | orrd 384 |
. 2
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13 | 12 | orri 382 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-ex 1675 df-nf 1679 |
This theorem is referenced by: (None) |
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