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Mirrors > Home > MPE Home > Th. List > 3p3e6 | Structured version Visualization version GIF version |
Description: 3 + 3 = 6. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
3p3e6 | ⊢ (3 + 3) = 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 11549 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 7027 | . . 3 ⊢ (3 + 3) = (3 + (2 + 1)) |
3 | 3cn 11566 | . . . 4 ⊢ 3 ∈ ℂ | |
4 | 2cn 11560 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 10441 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10497 | . . 3 ⊢ ((3 + 2) + 1) = (3 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2822 | . 2 ⊢ (3 + 3) = ((3 + 2) + 1) |
8 | df-6 11552 | . . 3 ⊢ 6 = (5 + 1) | |
9 | 3p2e5 11636 | . . . 4 ⊢ (3 + 2) = 5 | |
10 | 9 | oveq1i 7026 | . . 3 ⊢ ((3 + 2) + 1) = (5 + 1) |
11 | 8, 10 | eqtr4i 2822 | . 2 ⊢ 6 = ((3 + 2) + 1) |
12 | 7, 11 | eqtr4i 2822 | 1 ⊢ (3 + 3) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1522 (class class class)co 7016 1c1 10384 + caddc 10386 2c2 11540 3c3 11541 5c5 11543 6c6 11544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-8 2083 ax-9 2091 ax-10 2112 ax-11 2126 ax-12 2141 ax-ext 2769 ax-1cn 10441 ax-addcl 10443 ax-addass 10448 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-3an 1082 df-tru 1525 df-ex 1762 df-nf 1766 df-sb 2043 df-clab 2776 df-cleq 2788 df-clel 2863 df-nfc 2935 df-rex 3111 df-rab 3114 df-v 3439 df-dif 3862 df-un 3864 df-in 3866 df-ss 3874 df-nul 4212 df-if 4382 df-sn 4473 df-pr 4475 df-op 4479 df-uni 4746 df-br 4963 df-iota 6189 df-fv 6233 df-ov 7019 df-2 11548 df-3 11549 df-4 11550 df-5 11551 df-6 11552 |
This theorem is referenced by: 3t2e6 11651 163prm 16287 631prm 16289 2503prm 16302 binom4 25109 ex-dvds 27927 ex-gcd 27928 kur14lem8 32068 ex-decpmul 38700 gbegt5 43408 gboge9 43411 gbpart6 43413 gbpart9 43416 gbpart11 43417 zlmodzxzequa 44031 |
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