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Mirrors > Home > ILE Home > Th. List > iffalse | Unicode version |
Description: Value of the conditional operator when its first argument is false. (Contributed by NM, 14-Aug-1999.) |
Ref | Expression |
---|---|
iffalse |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedlemb 916 |
. . 3
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2 | 1 | abbi2dv 2206 |
. 2
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3 | df-if 3394 |
. 2
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4 | 2, 3 | syl6reqr 2139 |
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-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-if 3394 |
This theorem is referenced by: iffalsei 3402 iffalsed 3403 ifnefalse 3404 ifsbdc 3405 ifcldadc 3420 ifeq1dadc 3421 ifbothdadc 3422 ifbothdc 3423 ifiddc 3424 ifcldcd 3426 ifandc 3427 fidifsnen 6586 nnnninf 6806 uzin 9051 modifeq2int 9793 bcval 10157 bcval3 10159 isumrblem 10765 fisumcvg 10766 fsum3cvg 10767 isummolem2a 10771 sumsplitdc 10826 flodddiv4 11212 gcdn0val 11231 dfgcd2 11281 lcmn0val 11326 |
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