Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 5p5e10 | Unicode version |
Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.) |
Ref | Expression |
---|---|
5p5e10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 7976 | . . . 4 | |
2 | 1 | oveq2i 5523 | . . 3 |
3 | 5cn 7995 | . . . 4 | |
4 | 4cn 7993 | . . . 4 | |
5 | ax-1cn 6977 | . . . 4 | |
6 | 3, 4, 5 | addassi 7035 | . . 3 |
7 | 2, 6 | eqtr4i 2063 | . 2 |
8 | df-10 7981 | . . 3 | |
9 | 5p4e9 8059 | . . . 4 | |
10 | 9 | oveq1i 5522 | . . 3 |
11 | 8, 10 | eqtr4i 2063 | . 2 |
12 | 7, 11 | eqtr4i 2063 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 (class class class)co 5512 c1 6890 caddc 6892 c4 7966 c5 7967 c9 7971 c10 7972 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-resscn 6976 ax-1cn 6977 ax-1re 6978 ax-addrcl 6981 ax-addass 6986 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 df-2 7973 df-3 7974 df-4 7975 df-5 7976 df-6 7977 df-7 7978 df-8 7979 df-9 7980 df-10 7981 |
This theorem is referenced by: 5t2e10 8074 5t4e20 8442 |
Copyright terms: Public domain | W3C validator |