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Mirrors > Home > MPE Home > Th. List > Mathboxes > ifpor123g | Structured version Visualization version Unicode version |
Description: Disjunction of conditional logical operators. (Contributed by RP, 18-Apr-2020.) |
Ref | Expression |
---|---|
ifpor123g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-or 372 |
. . . 4
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2 | ifpnot23 36134 |
. . . . 5
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3 | 2 | imbi1i 327 |
. . . 4
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4 | 1, 3 | bitri 253 |
. . 3
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5 | ifpim123g 36156 |
. . 3
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6 | 4, 5 | bitri 253 |
. 2
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7 | pm4.64 374 |
. . . . 5
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8 | 7 | orbi2i 522 |
. . . 4
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9 | pm4.64 374 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9 | orbi2i 522 |
. . . 4
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11 | 8, 10 | anbi12i 704 |
. . 3
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12 | pm4.64 374 |
. . . . 5
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13 | 12 | orbi2i 522 |
. . . 4
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14 | pm4.64 374 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | orbi2i 522 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 13, 15 | anbi12i 704 |
. . 3
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17 | 11, 16 | anbi12i 704 |
. 2
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18 | 6, 17 | bitri 253 |
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-ifp 1428 |
This theorem is referenced by: (None) |
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