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Mirrors > Home > ILE Home > Th. List > 5p3e8 | GIF version |
Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
5p3e8 | ⊢ (5 + 3) = 8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8780 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 5785 | . . 3 ⊢ (5 + 3) = (5 + (2 + 1)) |
3 | 5cn 8800 | . . . 4 ⊢ 5 ∈ ℂ | |
4 | 2cn 8791 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 7713 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7774 | . . 3 ⊢ ((5 + 2) + 1) = (5 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2163 | . 2 ⊢ (5 + 3) = ((5 + 2) + 1) |
8 | df-8 8785 | . . 3 ⊢ 8 = (7 + 1) | |
9 | 5p2e7 8866 | . . . 4 ⊢ (5 + 2) = 7 | |
10 | 9 | oveq1i 5784 | . . 3 ⊢ ((5 + 2) + 1) = (7 + 1) |
11 | 8, 10 | eqtr4i 2163 | . 2 ⊢ 8 = ((5 + 2) + 1) |
12 | 7, 11 | eqtr4i 2163 | 1 ⊢ (5 + 3) = 8 |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 (class class class)co 5774 1c1 7621 + caddc 7623 2c2 8771 3c3 8772 5c5 8774 7c7 8776 8c8 8777 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-resscn 7712 ax-1cn 7713 ax-1re 7714 ax-addrcl 7717 ax-addass 7722 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 df-2 8779 df-3 8780 df-4 8781 df-5 8782 df-6 8783 df-7 8784 df-8 8785 |
This theorem is referenced by: 5p4e9 8868 ef01bndlem 11463 |
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