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Mirrors > Home > ILE Home > Th. List > iftrued | Unicode version |
Description: Value of the conditional operator when its first argument is true. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
iftrued.1 |
Ref | Expression |
---|---|
iftrued |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iftrued.1 | . 2 | |
2 | iftrue 3449 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 cif 3444 |
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 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-if 3445 |
This theorem is referenced by: eqifdc 3476 mposnif 5833 fimax2gtrilemstep 6762 updjudhcoinlf 6933 omp1eomlem 6947 difinfsnlem 6952 ctssdclemn0 6963 ctssdc 6966 enumctlemm 6967 fodju0 6987 iseqf1olemnab 10216 iseqf1olemab 10217 iseqf1olemqk 10222 iseqf1olemfvp 10225 seq3f1olemqsumkj 10226 seq3f1olemqsum 10228 seq3f1oleml 10231 seq3f1o 10232 fser0const 10244 expnnval 10251 2zsupmax 10952 xrmaxifle 10970 xrmaxiflemab 10971 xrmaxiflemlub 10972 xrmaxiflemcom 10973 summodclem3 11104 summodclem2a 11105 isum 11109 fsum3 11111 isumss 11115 fsumcl2lem 11122 fsumadd 11130 fsummulc2 11172 cvgratz 11256 ef0lem 11280 gcdval 11560 ennnfonelemss 11834 ennnfonelemkh 11836 ennnfonelemhf1o 11837 ressid2 11929 subctctexmid 13092 nninfalllemn 13098 nninfsellemeq 13106 nninfsellemeqinf 13108 nninffeq 13112 |
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