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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 667 |
. . . . 5
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3 | 2 | anbi2d 464 |
. . . 4
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4 | 1, 3 | orbi12d 794 |
. . 3
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5 | 4 | abbidv 2311 |
. 2
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6 | df-if 3558 |
. 2
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7 | df-if 3558 |
. 2
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8 | 5, 6, 7 | 3eqtr4g 2251 |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-if 3558 |
This theorem is referenced by: ifbid 3578 ifbieq2i 3580 ifnebibdc 3600 fodjuomni 7208 fodjumkv 7219 nninfwlpoimlemg 7234 1tonninf 10512 lgsdi 15153 nninfsellemqall 15505 nninfomni 15509 |
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