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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 467 |
. . . 4
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2 | notbi 666 |
. . . . 5
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3 | 2 | anbi2d 464 |
. . . 4
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4 | 1, 3 | orbi12d 793 |
. . 3
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5 | 4 | abbidv 2295 |
. 2
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6 | df-if 3535 |
. 2
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7 | df-if 3535 |
. 2
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8 | 5, 6, 7 | 3eqtr4g 2235 |
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-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-if 3535 |
This theorem is referenced by: ifbid 3555 ifbieq2i 3557 fodjuomni 7144 fodjumkv 7155 nninfwlpoimlemg 7170 1tonninf 10435 lgsdi 14309 nninfsellemqall 14624 nninfomni 14628 |
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