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Mirrors > Home > MPE Home > Th. List > 7p2e9 | Structured version Visualization version GIF version |
Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
7p2e9 | ⊢ (7 + 2) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 11079 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 6661 | . . . 4 ⊢ (7 + 2) = (7 + (1 + 1)) |
3 | 7cn 11104 | . . . . 5 ⊢ 7 ∈ ℂ | |
4 | ax-1cn 9994 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 10048 | . . . 4 ⊢ ((7 + 1) + 1) = (7 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2647 | . . 3 ⊢ (7 + 2) = ((7 + 1) + 1) |
7 | df-8 11085 | . . . 4 ⊢ 8 = (7 + 1) | |
8 | 7 | oveq1i 6660 | . . 3 ⊢ (8 + 1) = ((7 + 1) + 1) |
9 | 6, 8 | eqtr4i 2647 | . 2 ⊢ (7 + 2) = (8 + 1) |
10 | df-9 11086 | . 2 ⊢ 9 = (8 + 1) | |
11 | 9, 10 | eqtr4i 2647 | 1 ⊢ (7 + 2) = 9 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 1c1 9937 + caddc 9939 2c2 11070 7c7 11075 8c8 11076 9c9 11077 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-addass 10001 ax-i2m1 10004 ax-1ne0 10005 ax-rrecex 10008 ax-cnre 10009 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-2 11079 df-3 11080 df-4 11081 df-5 11082 df-6 11083 df-7 11084 df-8 11085 df-9 11086 |
This theorem is referenced by: 7p3e10OLD 11173 7p3e10 11603 7t7e49 11653 cos2bnd 14918 prmlem2 15827 139prm 15831 1259lem2 15839 1259lem3 15840 1259lem4 15841 1259lem5 15842 2503lem2 15845 4001lem4 15851 hgt750lem2 30730 fmtno5lem4 41468 fmtno5fac 41494 139prmALT 41511 |
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