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Mirrors > Home > ILE Home > Th. List > adddiri | Unicode version |
Description: Distributive law (right-distributivity). (Contributed by NM, 16-Feb-1995.) |
Ref | Expression |
---|---|
axi.1 | |
axi.2 | |
axi.3 |
Ref | Expression |
---|---|
adddiri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.1 | . 2 | |
2 | axi.2 | . 2 | |
3 | axi.3 | . 2 | |
4 | adddir 7898 | . 2 | |
5 | 1, 2, 3, 4 | mp3an 1332 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wcel 2141 (class class class)co 5850 cc 7759 caddc 7764 cmul 7766 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-addcl 7857 ax-mulcom 7862 ax-distr 7865 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-iota 5158 df-fv 5204 df-ov 5853 |
This theorem is referenced by: numma 9373 binom2i 10571 3dvdsdec 11811 3dvds2dec 11812 sincosq3sgn 13502 sincosq4sgn 13503 cosq23lt0 13507 |
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