Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > decbin2 | Unicode version |
Description: Decompose base 4 into base 2. (Contributed by Mario Carneiro, 18-Feb-2014.) |
Ref | Expression |
---|---|
decbin.1 |
Ref | Expression |
---|---|
decbin2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2t1e2 9001 | . . 3 | |
2 | 1 | oveq2i 5847 | . 2 |
3 | 2cn 8919 | . . 3 | |
4 | decbin.1 | . . . . 5 | |
5 | 4 | nn0cni 9117 | . . . 4 |
6 | 3, 5 | mulcli 7895 | . . 3 |
7 | ax-1cn 7837 | . . 3 | |
8 | 3, 6, 7 | adddii 7900 | . 2 |
9 | 4 | decbin0 9452 | . . 3 |
10 | 9 | oveq1i 5846 | . 2 |
11 | 2, 8, 10 | 3eqtr4ri 2196 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 (class class class)co 5836 c1 7745 caddc 7747 cmul 7749 c2 8899 c4 8901 cn0 9105 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4094 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-mulcom 7845 ax-addass 7846 ax-mulass 7847 ax-distr 7848 ax-1rid 7851 ax-rnegex 7853 ax-cnre 7855 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 df-inn 8849 df-2 8907 df-3 8908 df-4 8909 df-n0 9106 |
This theorem is referenced by: decbin3 9454 |
Copyright terms: Public domain | W3C validator |