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Mirrors > Home > ILE Home > Th. List > iftrue | Unicode version |
Description: Value of the conditional operator when its first argument is true. (Contributed by NM, 15-May-1999.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
iftrue |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-if 3536 |
. 2
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2 | dedlema 969 |
. . 3
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3 | 2 | abbi2dv 2296 |
. 2
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4 | 1, 3 | eqtr4id 2229 |
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-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-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-if 3536 |
This theorem is referenced by: iftruei 3541 iftrued 3542 ifsbdc 3547 ifcldadc 3564 ifbothdadc 3567 ifbothdc 3568 ifiddc 3569 ifcldcd 3571 ifnotdc 3572 ifandc 3573 ifordc 3574 fidifsnen 6870 nnnninf 7124 nnnninf2 7125 mkvprop 7156 uzin 9560 fzprval 10082 fztpval 10083 modifeq2int 10386 bcval 10729 bcval2 10730 sumrbdclem 11385 fsum3cvg 11386 summodclem2a 11389 isumss2 11401 fsum3ser 11405 fsumsplit 11415 sumsplitdc 11440 prodrbdclem 11579 fproddccvg 11580 iprodap 11588 iprodap0 11590 prodssdc 11597 fprodsplitdc 11604 flodddiv4 11939 gcd0val 11961 dfgcd2 12015 eucalgf 12055 eucalginv 12056 eucalglt 12057 phisum 12240 pc0 12304 pcgcd 12328 pcmptcl 12340 pcmpt 12341 pcmpt2 12342 pcprod 12344 fldivp1 12346 1arithlem4 12364 unct 12443 xpsfrnel 12763 dvexp2 14179 lgsval2lem 14414 lgsneg 14428 lgsdilem 14431 lgsdir2 14437 lgsdir 14439 lgsdi 14441 lgsne0 14442 nnsf 14757 nninfsellemsuc 14764 |
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