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Mirrors > Home > ILE Home > Th. List > adddii | Unicode version |
Description: Distributive law (left-distributivity). (Contributed by NM, 23-Nov-1994.) |
Ref | Expression |
---|---|
axi.1 | |
axi.2 | |
axi.3 |
Ref | Expression |
---|---|
adddii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.1 | . 2 | |
2 | axi.2 | . 2 | |
3 | axi.3 | . 2 | |
4 | adddi 7752 | . 2 | |
5 | 1, 2, 3, 4 | mp3an 1315 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 (class class class)co 5774 cc 7618 caddc 7623 cmul 7625 |
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-distr 7724 |
This theorem depends on definitions: df-bi 116 df-3an 964 |
This theorem is referenced by: 3t3e9 8877 numltc 9207 numsucc 9221 numma 9225 decmul10add 9250 4t3lem 9278 9t11e99 9311 decbin2 9322 binom2i 10401 3dec 10461 3dvds2dec 11563 |
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