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Mirrors > Home > MPE Home > Th. List > 4p3e7 | Structured version Visualization version GIF version |
Description: 4 + 3 = 7. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
4p3e7 | ⊢ (4 + 3) = 7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 11689 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 7156 | . . 3 ⊢ (4 + 3) = (4 + (2 + 1)) |
3 | 4cn 11710 | . . . 4 ⊢ 4 ∈ ℂ | |
4 | 2cn 11700 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 10583 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10639 | . . 3 ⊢ ((4 + 2) + 1) = (4 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2844 | . 2 ⊢ (4 + 3) = ((4 + 2) + 1) |
8 | df-7 11693 | . . 3 ⊢ 7 = (6 + 1) | |
9 | 4p2e6 11778 | . . . 4 ⊢ (4 + 2) = 6 | |
10 | 9 | oveq1i 7155 | . . 3 ⊢ ((4 + 2) + 1) = (6 + 1) |
11 | 8, 10 | eqtr4i 2844 | . 2 ⊢ 7 = ((4 + 2) + 1) |
12 | 7, 11 | eqtr4i 2844 | 1 ⊢ (4 + 3) = 7 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 (class class class)co 7145 1c1 10526 + caddc 10528 2c2 11680 3c3 11681 4c4 11682 6c6 11684 7c7 11685 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-1cn 10583 ax-addcl 10585 ax-addass 10590 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-ov 7148 df-2 11688 df-3 11689 df-4 11690 df-5 11691 df-6 11692 df-7 11693 |
This theorem is referenced by: 4p4e8 11780 37prm 16442 317prm 16447 1259lem5 16456 2503lem2 16459 4001lem1 16462 4001lem2 16463 log2ub 25454 bposlem8 25794 2lgslem3d 25902 2lgsoddprmlem3d 25916 hgt750lem 31821 hgt750lem2 31822 fmtno5lem4 43595 257prm 43600 127prm 43640 gbpart7 43809 sbgoldbwt 43819 sbgoldbst 43820 |
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