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Mirrors > Home > ILE Home > Th. List > 7p3e10 | GIF version |
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
7p3e10 | ⊢ (7 + 3) = ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8908 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 5847 | . . 3 ⊢ (7 + 3) = (7 + (2 + 1)) |
3 | 7cn 8932 | . . . 4 ⊢ 7 ∈ ℂ | |
4 | 2cn 8919 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 7837 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7898 | . . 3 ⊢ ((7 + 2) + 1) = (7 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2188 | . 2 ⊢ (7 + 3) = ((7 + 2) + 1) |
8 | 7p2e9 8999 | . . 3 ⊢ (7 + 2) = 9 | |
9 | 8 | oveq1i 5846 | . 2 ⊢ ((7 + 2) + 1) = (9 + 1) |
10 | 9p1e10 9315 | . 2 ⊢ (9 + 1) = ;10 | |
11 | 7, 9, 10 | 3eqtri 2189 | 1 ⊢ (7 + 3) = ;10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1342 (class class class)co 5836 0cc0 7744 1c1 7745 + caddc 7747 2c2 8899 3c3 8900 7c7 8904 9c9 8906 ;cdc 9313 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4094 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-mulcom 7845 ax-addass 7846 ax-mulass 7847 ax-distr 7848 ax-1rid 7851 ax-0id 7852 ax-cnre 7855 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 df-inn 8849 df-2 8907 df-3 8908 df-4 8909 df-5 8910 df-6 8911 df-7 8912 df-8 8913 df-9 8914 df-dec 9314 |
This theorem is referenced by: 7p4e11 9388 |
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