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Mirrors > Home > ILE Home > Th. List > 3p3e6 | GIF version |
Description: 3 + 3 = 6. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
3p3e6 | ⊢ (3 + 3) = 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 9010 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 5908 | . . 3 ⊢ (3 + 3) = (3 + (2 + 1)) |
3 | 3cn 9025 | . . . 4 ⊢ 3 ∈ ℂ | |
4 | 2cn 9021 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 7935 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7996 | . . 3 ⊢ ((3 + 2) + 1) = (3 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2213 | . 2 ⊢ (3 + 3) = ((3 + 2) + 1) |
8 | df-6 9013 | . . 3 ⊢ 6 = (5 + 1) | |
9 | 3p2e5 9091 | . . . 4 ⊢ (3 + 2) = 5 | |
10 | 9 | oveq1i 5907 | . . 3 ⊢ ((3 + 2) + 1) = (5 + 1) |
11 | 8, 10 | eqtr4i 2213 | . 2 ⊢ 6 = ((3 + 2) + 1) |
12 | 7, 11 | eqtr4i 2213 | 1 ⊢ (3 + 3) = 6 |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 (class class class)co 5897 1c1 7843 + caddc 7845 2c2 9001 3c3 9002 5c5 9004 6c6 9005 |
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 7934 ax-1cn 7935 ax-1re 7936 ax-addrcl 7939 ax-addass 7944 |
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 5196 df-fv 5243 df-ov 5900 df-2 9009 df-3 9010 df-4 9011 df-5 9012 df-6 9013 |
This theorem is referenced by: 3t2e6 9106 binom4 14874 ex-dvds 14960 ex-gcd 14961 |
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