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Mirrors > Home > NFE 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedlem0a 918 | . . 3 | |
2 | 1 | abbi2dv 2468 | . 2 |
3 | dfif2 3664 | . 2 | |
4 | 2, 3 | syl6reqr 2404 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wceq 1642 wcel 1710 cab 2339 cif 3662 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-if 3663 |
This theorem is referenced by: ifsb 3671 ifbi 3679 ifeq2da 3688 ifclda 3689 elimif 3691 ifbothda 3692 ifid 3694 ifeqor 3699 ifnot 3700 ifan 3701 ifor 3702 dedth 3703 elimhyp 3710 elimhyp2v 3711 elimhyp3v 3712 elimhyp4v 3713 elimdhyp 3715 keephyp2v 3717 keephyp3v 3718 setswith 4321 dfiota3 4370 eqtfinrelk 4486 tfinnul 4491 dfphi2 4569 phi11lem1 4595 0cnelphi 4597 phialllem1 4616 elimdelov 5573 enprmaplem5 6080 |
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