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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedlemb 877 | . . 3 | |
2 | 1 | abbi2dv 2156 | . 2 |
3 | df-if 3332 | . 2 | |
4 | 2, 3 | syl6reqr 2091 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wo 629 wceq 1243 wcel 1393 cab 2026 cif 3331 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-if 3332 |
This theorem is referenced by: iffalsei 3340 iffalsed 3341 ifnefalse 3342 ifbothdc 3357 ifcldcd 3358 fidifsnen 6331 uzin 8505 expival 9257 |
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