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Mirrors > Home > MPE Home > Th. List > ifbi | Structured version Visualization version Unicode version |
Description: Equivalence theorem for conditional operators. (Contributed by Raph Levien, 15-Jan-2004.) |
Ref | Expression |
---|---|
ifbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi3 994 | . 2 | |
2 | iftrue 4092 | . . . 4 | |
3 | iftrue 4092 | . . . . 5 | |
4 | 3 | eqcomd 2628 | . . . 4 |
5 | 2, 4 | sylan9eq 2676 | . . 3 |
6 | iffalse 4095 | . . . 4 | |
7 | iffalse 4095 | . . . . 5 | |
8 | 7 | eqcomd 2628 | . . . 4 |
9 | 6, 8 | sylan9eq 2676 | . . 3 |
10 | 5, 9 | jaoi 394 | . 2 |
11 | 1, 10 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wo 383 wa 384 wceq 1483 cif 4086 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-if 4087 |
This theorem is referenced by: ifbid 4108 ifbieq2i 4110 gsummoncoe1 19674 scmatscm 20319 mulmarep1gsum1 20379 madugsum 20449 mp2pm2mplem4 20614 dchrhash 24996 lgsdi 25059 rpvmasum2 25201 bj-projval 32984 matunitlindflem2 33406 itg2gt0cn 33465 dedths 34248 |
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