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Mirrors > Home > ILE Home > Th. List > ifordc | Unicode version |
Description: Rewrite a disjunction in a conditional as two nested conditionals. (Contributed by Mario Carneiro, 28-Jul-2014.) |
Ref | Expression |
---|---|
ifordc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmiddc 836 |
. 2
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2 | iftrue 3539 |
. . . . 5
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3 | 2 | orcs 735 |
. . . 4
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4 | iftrue 3539 |
. . . 4
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5 | 3, 4 | eqtr4d 2213 |
. . 3
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6 | iffalse 3542 |
. . . 4
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7 | biorf 744 |
. . . . 5
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8 | 7 | ifbid 3555 |
. . . 4
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9 | 6, 8 | eqtr2d 2211 |
. . 3
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10 | 5, 9 | jaoi 716 |
. 2
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11 | 1, 10 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-if 3535 |
This theorem is referenced by: nninfwlpoimlemg 7172 |
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