![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 8p2e10 | GIF version |
Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
8p2e10 | ⊢ (8 + 2) = ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8803 | . . . 4 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5793 | . . 3 ⊢ (8 + 2) = (8 + (1 + 1)) |
3 | 8cn 8830 | . . . 4 ⊢ 8 ∈ ℂ | |
4 | ax-1cn 7737 | . . . 4 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7798 | . . 3 ⊢ ((8 + 1) + 1) = (8 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2164 | . 2 ⊢ (8 + 2) = ((8 + 1) + 1) |
7 | df-9 8810 | . . 3 ⊢ 9 = (8 + 1) | |
8 | 7 | oveq1i 5792 | . 2 ⊢ (9 + 1) = ((8 + 1) + 1) |
9 | 9p1e10 9208 | . 2 ⊢ (9 + 1) = ;10 | |
10 | 6, 8, 9 | 3eqtr2i 2167 | 1 ⊢ (8 + 2) = ;10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1332 (class class class)co 5782 0cc0 7644 1c1 7645 + caddc 7647 2c2 8795 8c8 8801 9c9 8802 ;cdc 9206 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-cnex 7735 ax-resscn 7736 ax-1cn 7737 ax-1re 7738 ax-icn 7739 ax-addcl 7740 ax-addrcl 7741 ax-mulcl 7742 ax-mulcom 7745 ax-addass 7746 ax-mulass 7747 ax-distr 7748 ax-1rid 7751 ax-0id 7752 ax-cnre 7755 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 df-inn 8745 df-2 8803 df-3 8804 df-4 8805 df-5 8806 df-6 8807 df-7 8808 df-8 8809 df-9 8810 df-dec 9207 |
This theorem is referenced by: 8p3e11 9286 8t5e40 9323 |
Copyright terms: Public domain | W3C validator |