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Mathbox for Richard Penner |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ifpananb | Structured version Visualization version Unicode version |
Description: Factor conditional logic operator over conjunction in terms 2 and 3. (Contributed by RP, 21-Apr-2020.) |
Ref | Expression |
---|---|
ifpananb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anor 497 |
. . 3
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2 | anor 497 |
. . 3
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3 | ifpbi23 36187 |
. . 3
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4 | 1, 2, 3 | mp2an 686 |
. 2
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5 | ifpororb 36220 |
. . . . 5
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6 | ifpnotnotb 36194 |
. . . . . 6
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7 | ifpnotnotb 36194 |
. . . . . 6
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8 | 6, 7 | orbi12i 530 |
. . . . 5
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9 | 5, 8 | bitri 257 |
. . . 4
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10 | 9 | notbii 303 |
. . 3
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11 | ifpnotnotb 36194 |
. . 3
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12 | anor 497 |
. . 3
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13 | 10, 11, 12 | 3bitr4i 285 |
. 2
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14 | 4, 13 | bitri 257 |
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 190 df-or 377 df-an 378 df-ifp 984 |
This theorem is referenced by: ifpnannanb 36222 |
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