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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 456 |
. . . 4
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2 | id 19 |
. . . . . 6
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3 | 2 | notbid 628 |
. . . . 5
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4 | 3 | anbi2d 453 |
. . . 4
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5 | 1, 4 | orbi12d 743 |
. . 3
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6 | 5 | abbidv 2206 |
. 2
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7 | df-if 3398 |
. 2
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8 | df-if 3398 |
. 2
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9 | 6, 7, 8 | 3eqtr4g 2146 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-if 3398 |
This theorem is referenced by: ifbid 3416 ifbieq2i 3418 fodjuomni 6865 1tonninf 9907 nninfsellemqall 12179 nninfomni 12183 |
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