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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 2600 are fairly straightforward consequences of axc9 2302. But in intuitionistic logic, it is not easy to add the extra to axi12 2600 and so we treat the two as separate axioms. (Contributed by Jim Kingdon, 22-Mar-2018.) |
Ref | Expression |
---|---|
axbnd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnae 2318 | . . . . . 6 | |
2 | nfnae 2318 | . . . . . 6 | |
3 | 1, 2 | nfan 1828 | . . . . 5 |
4 | nfnae 2318 | . . . . . . 7 | |
5 | nfnae 2318 | . . . . . . 7 | |
6 | 4, 5 | nfan 1828 | . . . . . 6 |
7 | axc9 2302 | . . . . . . 7 | |
8 | 7 | imp 445 | . . . . . 6 |
9 | 6, 8 | alrimi 2082 | . . . . 5 |
10 | 3, 9 | alrimi 2082 | . . . 4 |
11 | 10 | ex 450 | . . 3 |
12 | 11 | orrd 393 | . 2 |
13 | 12 | orri 391 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 wa 384 wal 1481 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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