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Mirrors > Home > MPE Home > Th. List > nanbi | Structured version Visualization version Unicode version |
Description: Show equivalence between the biconditional and the Nicod version. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof shortened by Wolf Lammen, 27-Jun-2020.) |
Ref | Expression |
---|---|
nanbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi3 904 |
. . 3
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2 | df-or 372 |
. . 3
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3 | df-nan 1385 |
. . . . 5
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4 | 3 | bicomi 206 |
. . . 4
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5 | nannot 1392 |
. . . . 5
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6 | nannot 1392 |
. . . . 5
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7 | 5, 6 | anbi12i 703 |
. . . 4
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8 | 4, 7 | imbi12i 328 |
. . 3
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9 | 1, 2, 8 | 3bitri 275 |
. 2
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10 | nannan 1389 |
. 2
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11 | 9, 10 | bitr4i 256 |
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 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-nan 1385 |
This theorem is referenced by: nic-dfim 1552 nic-dfneg 1553 |
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