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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 463 |
. . . 4
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2 | notbi 656 |
. . . . 5
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3 | 2 | anbi2d 460 |
. . . 4
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4 | 1, 3 | orbi12d 783 |
. . 3
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5 | 4 | abbidv 2258 |
. 2
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6 | df-if 3480 |
. 2
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7 | df-if 3480 |
. 2
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8 | 5, 6, 7 | 3eqtr4g 2198 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-if 3480 |
This theorem is referenced by: ifbid 3498 ifbieq2i 3500 fodjuomni 7029 fodjumkv 7042 1tonninf 10244 nninfsellemqall 13386 nninfomni 13390 |
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