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Mirrors > Home > MPE Home > Th. List > ifsb | Structured version Visualization version Unicode version |
Description: Distribute a function over an if-clause. (Contributed by Mario Carneiro, 14-Aug-2013.) |
Ref | Expression |
---|---|
ifsb.1 | |
ifsb.2 |
Ref | Expression |
---|---|
ifsb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iftrue 4092 | . . . 4 | |
2 | ifsb.1 | . . . 4 | |
3 | 1, 2 | syl 17 | . . 3 |
4 | iftrue 4092 | . . 3 | |
5 | 3, 4 | eqtr4d 2659 | . 2 |
6 | iffalse 4095 | . . . 4 | |
7 | ifsb.2 | . . . 4 | |
8 | 6, 7 | syl 17 | . . 3 |
9 | iffalse 4095 | . . 3 | |
10 | 8, 9 | eqtr4d 2659 | . 2 |
11 | 5, 10 | pm2.61i 176 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 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: fvif 6204 iffv 6205 ovif 6737 ovif2 6738 ifov 6740 xmulneg1 12099 efrlim 24696 lgsneg 25046 lgsdilem 25049 rpvmasum2 25201 |
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