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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 | df-if 3480 |
. 2
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2 | dedlemb 955 |
. . 3
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3 | 2 | abbi2dv 2259 |
. 2
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4 | 1, 3 | eqtr4id 2192 |
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-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-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-if 3480 |
This theorem is referenced by: iffalsei 3488 iffalsed 3489 ifnefalse 3490 ifsbdc 3491 ifcldadc 3506 ifeq1dadc 3507 ifbothdadc 3508 ifbothdc 3509 ifiddc 3510 ifcldcd 3512 ifandc 3513 fidifsnen 6772 nnnninf 7031 uzin 9382 modifeq2int 10190 bcval 10527 bcval3 10529 sumrbdclem 11178 fsum3cvg 11179 summodclem2a 11182 sumsplitdc 11233 prodrbdclem 11372 fproddccvg 11373 flodddiv4 11667 gcdn0val 11686 dfgcd2 11738 lcmn0val 11783 unct 11991 |
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