Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > 5p3e8 | Structured version Visualization version 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 11704 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 7170 | . . 3 ⊢ (5 + 3) = (5 + (2 + 1)) |
3 | 5cn 11728 | . . . 4 ⊢ 5 ∈ ℂ | |
4 | 2cn 11715 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 10598 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10654 | . . 3 ⊢ ((5 + 2) + 1) = (5 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2850 | . 2 ⊢ (5 + 3) = ((5 + 2) + 1) |
8 | df-8 11709 | . . 3 ⊢ 8 = (7 + 1) | |
9 | 5p2e7 11796 | . . . 4 ⊢ (5 + 2) = 7 | |
10 | 9 | oveq1i 7169 | . . 3 ⊢ ((5 + 2) + 1) = (7 + 1) |
11 | 8, 10 | eqtr4i 2850 | . 2 ⊢ 8 = ((5 + 2) + 1) |
12 | 7, 11 | eqtr4i 2850 | 1 ⊢ (5 + 3) = 8 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 (class class class)co 7159 1c1 10541 + caddc 10543 2c2 11695 3c3 11696 5c5 11698 7c7 11700 8c8 11701 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2796 ax-1cn 10598 ax-addcl 10600 ax-addass 10605 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2966 df-rab 3150 df-v 3499 df-dif 3942 df-un 3944 df-in 3946 df-ss 3955 df-nul 4295 df-if 4471 df-sn 4571 df-pr 4573 df-op 4577 df-uni 4842 df-br 5070 df-iota 6317 df-fv 6366 df-ov 7162 df-2 11703 df-3 11704 df-4 11705 df-5 11706 df-6 11707 df-7 11708 df-8 11709 |
This theorem is referenced by: 5p4e9 11798 ef01bndlem 15540 2exp16 16427 1259lem2 16468 log2ublem3 25529 log2ub 25530 bposlem8 25870 lgsdir2lem1 25904 fib6 31668 235t711 39183 ex-decpmul 39184 fmtno5lem2 43723 fmtno5lem4 43725 257prm 43730 gbpart8 43940 8gbe 43945 evengpop3 43970 |
Copyright terms: Public domain | W3C validator |