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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 12330 | . . . . 5 ⊢ 2 = (1 + 1) | |
| 2 | 1 | oveq2i 7443 | . . . 4 ⊢ (4 + 2) = (4 + (1 + 1)) | 
| 3 | 4cn 12352 | . . . . 5 ⊢ 4 ∈ ℂ | |
| 4 | ax-1cn 11214 | . . . . 5 ⊢ 1 ∈ ℂ | |
| 5 | 3, 4, 4 | addassi 11272 | . . . 4 ⊢ ((4 + 1) + 1) = (4 + (1 + 1)) | 
| 6 | 2, 5 | eqtr4i 2767 | . . 3 ⊢ (4 + 2) = ((4 + 1) + 1) | 
| 7 | df-5 12333 | . . . 4 ⊢ 5 = (4 + 1) | |
| 8 | 7 | oveq1i 7442 | . . 3 ⊢ (5 + 1) = ((4 + 1) + 1) | 
| 9 | 6, 8 | eqtr4i 2767 | . 2 ⊢ (4 + 2) = (5 + 1) | 
| 10 | df-6 12334 | . 2 ⊢ 6 = (5 + 1) | |
| 11 | 9, 10 | eqtr4i 2767 | 1 ⊢ (4 + 2) = 6 | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1539 (class class class)co 7432 1c1 11157 + caddc 11159 2c2 12322 4c4 12324 5c5 12325 6c6 12326 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-1cn 11214 ax-addcl 11216 ax-addass 11221 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-iota 6513 df-fv 6568 df-ov 7435 df-2 12330 df-3 12331 df-4 12332 df-5 12333 df-6 12334 | 
| This theorem is referenced by: 4p3e7 12421 div4p1lem1div2 12523 4t4e16 12834 6gcd4e2 16576 2exp16 17129 163prm 17163 631prm 17165 1259lem4 17172 2503lem2 17176 2503lem3 17177 4001lem1 17179 4001lem2 17180 4001lem4 17182 bposlem9 27337 hgt750lem2 34668 3exp7 42055 3lexlogpow5ineq1 42056 aks4d1p1p5 42077 235t711 42344 ex-decpmul 42345 3cubeslem3r 42703 lhe4.4ex1a 44353 ceil5half3 47347 fmtno4prmfac 47564 fmtno5faclem1 47571 gbowgt5 47754 mogoldbb 47777 | 
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