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Mirrors > Home > ILE Home > Th. List > 3p2e5 | GIF version |
Description: 3 + 2 = 5. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
3p2e5 | ⊢ (3 + 2) = 5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8803 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5793 | . . . 4 ⊢ (3 + 2) = (3 + (1 + 1)) |
3 | 3cn 8819 | . . . . 5 ⊢ 3 ∈ ℂ | |
4 | ax-1cn 7737 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7798 | . . . 4 ⊢ ((3 + 1) + 1) = (3 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2164 | . . 3 ⊢ (3 + 2) = ((3 + 1) + 1) |
7 | df-4 8805 | . . . 4 ⊢ 4 = (3 + 1) | |
8 | 7 | oveq1i 5792 | . . 3 ⊢ (4 + 1) = ((3 + 1) + 1) |
9 | 6, 8 | eqtr4i 2164 | . 2 ⊢ (3 + 2) = (4 + 1) |
10 | df-5 8806 | . 2 ⊢ 5 = (4 + 1) | |
11 | 9, 10 | eqtr4i 2164 | 1 ⊢ (3 + 2) = 5 |
Colors of variables: wff set class |
Syntax hints: = wceq 1332 (class class class)co 5782 1c1 7645 + caddc 7647 2c2 8795 3c3 8796 4c4 8797 5c5 8798 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-resscn 7736 ax-1cn 7737 ax-1re 7738 ax-addrcl 7741 ax-addass 7746 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 df-2 8803 df-3 8804 df-4 8805 df-5 8806 |
This theorem is referenced by: 3p3e6 8886 |
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