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Mirrors > Home > MPE Home > Th. List > ovif2 | Structured version Visualization version Unicode version |
Description: Move a conditional outside of an operation. (Contributed by Thierry Arnoux, 1-Oct-2018.) |
Ref | Expression |
---|---|
ovif2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 6658 | . 2 | |
2 | oveq2 6658 | . 2 | |
3 | 1, 2 | ifsb 4099 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cif 4086 (class class class)co 6650 |
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-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 |
This theorem is referenced by: ramcl 15733 matsc 20256 scmatscmide 20313 mulmarep1el 20378 maducoeval2 20446 madugsum 20449 itg2const 23507 itg2monolem1 23517 iblmulc2 23597 itgmulc2lem1 23598 bddmulibl 23605 dchrvmasumiflem2 25191 rpvmasum2 25201 sgnneg 30602 itg2addnclem 33461 itgaddnclem2 33469 itgmulc2nclem1 33476 |
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