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Mirrors > Home > ILE Home > Th. List > 4p2e6 | 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 9003 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5903 | . . . 4 ⊢ (4 + 2) = (4 + (1 + 1)) |
3 | 4cn 9022 | . . . . 5 ⊢ 4 ∈ ℂ | |
4 | ax-1cn 7929 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7990 | . . . 4 ⊢ ((4 + 1) + 1) = (4 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2213 | . . 3 ⊢ (4 + 2) = ((4 + 1) + 1) |
7 | df-5 9006 | . . . 4 ⊢ 5 = (4 + 1) | |
8 | 7 | oveq1i 5902 | . . 3 ⊢ (5 + 1) = ((4 + 1) + 1) |
9 | 6, 8 | eqtr4i 2213 | . 2 ⊢ (4 + 2) = (5 + 1) |
10 | df-6 9007 | . 2 ⊢ 6 = (5 + 1) | |
11 | 9, 10 | eqtr4i 2213 | 1 ⊢ (4 + 2) = 6 |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 (class class class)co 5892 1c1 7837 + caddc 7839 2c2 8995 4c4 8997 5c5 8998 6c6 8999 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-resscn 7928 ax-1cn 7929 ax-1re 7930 ax-addrcl 7933 ax-addass 7938 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iota 5193 df-fv 5240 df-ov 5895 df-2 9003 df-3 9004 df-4 9005 df-5 9006 df-6 9007 |
This theorem is referenced by: 4p3e7 9088 div4p1lem1div2 9197 4t4e16 9507 6gcd4e2 12023 |
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