Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > adddid | Unicode version |
Description: Distributive law (left-distributivity). (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 | |
addcld.2 | |
addassd.3 |
Ref | Expression |
---|---|
adddid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 | . 2 | |
2 | addcld.2 | . 2 | |
3 | addassd.3 | . 2 | |
4 | adddi 7013 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 (class class class)co 5512 cc 6887 caddc 6892 cmul 6894 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-distr 6988 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: subdi 7382 mulreim 7595 apadd1 7599 conjmulap 7705 cju 7913 flhalf 9144 binom2 9362 binom3 9366 remim 9460 mulreap 9464 readd 9469 remullem 9471 imadd 9477 cjadd 9484 |
Copyright terms: Public domain | W3C validator |