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Mirrors > Home > ILE Home > Th. List > ifbi | Unicode version |
Description: Equivalence theorem for conditional operators. (Contributed by Raph Levien, 15-Jan-2004.) |
Ref | Expression |
---|---|
ifbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anbi2 455 |
. . . 4
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2 | id 19 |
. . . . . 6
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3 | 2 | notbid 625 |
. . . . 5
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4 | 3 | anbi2d 452 |
. . . 4
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5 | 1, 4 | orbi12d 740 |
. . 3
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6 | 5 | abbidv 2200 |
. 2
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7 | df-if 3374 |
. 2
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8 | df-if 3374 |
. 2
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9 | 6, 7, 8 | 3eqtr4g 2140 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-11 1438 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-if 3374 |
This theorem is referenced by: ifbid 3392 ifbieq2i 3394 fodjuomni 6709 1tonninf 9735 |
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