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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 3535 |
. 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 3535 |
This theorem is referenced by: iftruei 3540 iftrued 3541 ifsbdc 3546 ifcldadc 3563 ifbothdadc 3566 ifbothdc 3567 ifiddc 3568 ifcldcd 3570 ifnotdc 3571 ifandc 3572 ifordc 3573 fidifsnen 6867 nnnninf 7121 nnnninf2 7122 mkvprop 7153 uzin 9556 fzprval 10077 fztpval 10078 modifeq2int 10381 bcval 10722 bcval2 10723 sumrbdclem 11378 fsum3cvg 11379 summodclem2a 11382 isumss2 11394 fsum3ser 11398 fsumsplit 11408 sumsplitdc 11433 prodrbdclem 11572 fproddccvg 11573 iprodap 11581 iprodap0 11583 prodssdc 11590 fprodsplitdc 11597 flodddiv4 11931 gcd0val 11953 dfgcd2 12007 eucalgf 12047 eucalginv 12048 eucalglt 12049 phisum 12232 pc0 12296 pcgcd 12320 pcmptcl 12332 pcmpt 12333 pcmpt2 12334 pcprod 12336 fldivp1 12338 1arithlem4 12356 unct 12435 dvexp2 14047 lgsval2lem 14282 lgsneg 14296 lgsdilem 14299 lgsdir2 14305 lgsdir 14307 lgsdi 14309 lgsne0 14310 nnsf 14614 nninfsellemsuc 14621 |
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