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Mirrors > Home > MPE Home > Th. List > 3p2e5 | Structured version Visualization version 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 10956 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 6560 | . . . 4 ⊢ (3 + 2) = (3 + (1 + 1)) |
3 | 3cn 10972 | . . . . 5 ⊢ 3 ∈ ℂ | |
4 | ax-1cn 9873 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 9927 | . . . 4 ⊢ ((3 + 1) + 1) = (3 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2635 | . . 3 ⊢ (3 + 2) = ((3 + 1) + 1) |
7 | df-4 10958 | . . . 4 ⊢ 4 = (3 + 1) | |
8 | 7 | oveq1i 6559 | . . 3 ⊢ (4 + 1) = ((3 + 1) + 1) |
9 | 6, 8 | eqtr4i 2635 | . 2 ⊢ (3 + 2) = (4 + 1) |
10 | df-5 10959 | . 2 ⊢ 5 = (4 + 1) | |
11 | 9, 10 | eqtr4i 2635 | 1 ⊢ (3 + 2) = 5 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 (class class class)co 6549 1c1 9816 + caddc 9818 2c2 10947 3c3 10948 4c4 10949 5c5 10950 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-resscn 9872 ax-1cn 9873 ax-icn 9874 ax-addcl 9875 ax-addrcl 9876 ax-mulcl 9877 ax-mulrcl 9878 ax-addass 9880 ax-i2m1 9883 ax-1ne0 9884 ax-rrecex 9887 ax-cnre 9888 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-2 10956 df-3 10957 df-4 10958 df-5 10959 |
This theorem is referenced by: 3p3e6 11038 2exp16 15635 prmlem1a 15651 5prm 15653 prmlem2 15665 1259lem1 15676 1259lem4 15679 1259prm 15681 4001lem1 15686 4001lem4 15689 birthday 24481 ppiub 24729 bposlem6 24814 bposlem9 24817 2lgsoddprmlem3d 24938 ex-mod 26698 fib5 29794 kur14lem8 30449 problem1 30812 fmtnorec2 39993 fmtno5lem4 40006 257prm 40011 fmtno4nprmfac193 40024 2exp5 40045 41prothprmlem2 40073 linevalexample 41978 |
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