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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 8941 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5868 | . . . 4 ⊢ (4 + 2) = (4 + (1 + 1)) |
3 | 4cn 8960 | . . . . 5 ⊢ 4 ∈ ℂ | |
4 | ax-1cn 7871 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7932 | . . . 4 ⊢ ((4 + 1) + 1) = (4 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2195 | . . 3 ⊢ (4 + 2) = ((4 + 1) + 1) |
7 | df-5 8944 | . . . 4 ⊢ 5 = (4 + 1) | |
8 | 7 | oveq1i 5867 | . . 3 ⊢ (5 + 1) = ((4 + 1) + 1) |
9 | 6, 8 | eqtr4i 2195 | . 2 ⊢ (4 + 2) = (5 + 1) |
10 | df-6 8945 | . 2 ⊢ 6 = (5 + 1) | |
11 | 9, 10 | eqtr4i 2195 | 1 ⊢ (4 + 2) = 6 |
Colors of variables: wff set class |
Syntax hints: = wceq 1349 (class class class)co 5857 1c1 7779 + caddc 7781 2c2 8933 4c4 8935 5c5 8936 6c6 8937 |
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 705 ax-5 1441 ax-7 1442 ax-gen 1443 ax-ie1 1487 ax-ie2 1488 ax-8 1498 ax-10 1499 ax-11 1500 ax-i12 1501 ax-bndl 1503 ax-4 1504 ax-17 1520 ax-i9 1524 ax-ial 1528 ax-i5r 1529 ax-ext 2153 ax-resscn 7870 ax-1cn 7871 ax-1re 7872 ax-addrcl 7875 ax-addass 7880 |
This theorem depends on definitions: df-bi 116 df-3an 976 df-tru 1352 df-nf 1455 df-sb 1757 df-clab 2158 df-cleq 2164 df-clel 2167 df-nfc 2302 df-rex 2455 df-v 2733 df-un 3126 df-in 3128 df-ss 3135 df-sn 3590 df-pr 3591 df-op 3593 df-uni 3798 df-br 3991 df-iota 5162 df-fv 5208 df-ov 5860 df-2 8941 df-3 8942 df-4 8943 df-5 8944 df-6 8945 |
This theorem is referenced by: 4p3e7 9026 div4p1lem1div2 9135 4t4e16 9445 6gcd4e2 11954 |
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