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Mirrors > Home > MPE Home > Th. List > 4p2e6 | Structured version Visualization version GIF version |
Description: 4 + 2 = 6. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
4p2e6 | ⊢ (4 + 2) = 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 11688 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 7156 | . . . 4 ⊢ (4 + 2) = (4 + (1 + 1)) |
3 | 4cn 11710 | . . . . 5 ⊢ 4 ∈ ℂ | |
4 | ax-1cn 10583 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 10639 | . . . 4 ⊢ ((4 + 1) + 1) = (4 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2844 | . . 3 ⊢ (4 + 2) = ((4 + 1) + 1) |
7 | df-5 11691 | . . . 4 ⊢ 5 = (4 + 1) | |
8 | 7 | oveq1i 7155 | . . 3 ⊢ (5 + 1) = ((4 + 1) + 1) |
9 | 6, 8 | eqtr4i 2844 | . 2 ⊢ (4 + 2) = (5 + 1) |
10 | df-6 11692 | . 2 ⊢ 6 = (5 + 1) | |
11 | 9, 10 | eqtr4i 2844 | 1 ⊢ (4 + 2) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 (class class class)co 7145 1c1 10526 + caddc 10528 2c2 11680 4c4 11682 5c5 11683 6c6 11684 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-1cn 10583 ax-addcl 10585 ax-addass 10590 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-ov 7148 df-2 11688 df-3 11689 df-4 11690 df-5 11691 df-6 11692 |
This theorem is referenced by: 4p3e7 11779 div4p1lem1div2 11880 4t4e16 12185 6gcd4e2 15874 2exp16 16412 163prm 16446 631prm 16448 1259lem4 16455 2503lem2 16459 2503lem3 16460 4001lem1 16462 4001lem2 16463 4001lem4 16465 bposlem9 25795 hgt750lem2 31822 235t711 39055 ex-decpmul 39056 3cubeslem3r 39162 lhe4.4ex1a 40538 fmtno4prmfac 43611 fmtno5faclem1 43618 gbowgt5 43804 mogoldbb 43827 |
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