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Mirrors > Home > MPE Home > Th. List > cases2 | Structured version Visualization version Unicode version |
Description: Case disjunction
according to the value of ![]() |
Ref | Expression |
---|---|
cases2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.4 568 |
. . . 4
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2 | pm2.24 113 |
. . . . 5
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3 | 2 | adantr 471 |
. . . 4
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4 | 1, 3 | jca 539 |
. . 3
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5 | pm2.21 112 |
. . . . 5
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6 | 5 | adantr 471 |
. . . 4
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7 | pm3.4 568 |
. . . 4
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8 | 6, 7 | jca 539 |
. . 3
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9 | 4, 8 | jaoi 385 |
. 2
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10 | pm2.27 40 |
. . . . . 6
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11 | 10 | imdistani 701 |
. . . . 5
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12 | 11 | orcd 398 |
. . . 4
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13 | 12 | adantrr 728 |
. . 3
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14 | pm2.27 40 |
. . . . . 6
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15 | 14 | imdistani 701 |
. . . . 5
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16 | 15 | olcd 399 |
. . . 4
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17 | 16 | adantrl 727 |
. . 3
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18 | 13, 17 | pm2.61ian 804 |
. 2
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19 | 9, 18 | impbii 192 |
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 376 df-an 377 |
This theorem is referenced by: dfifp2 1437 ifval 3932 ifpidg 36181 ifpim123g 36190 |
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