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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 11080 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 6661 | . . 3 ⊢ (4 + 3) = (4 + (2 + 1)) |
3 | 4cn 11098 | . . . 4 ⊢ 4 ∈ ℂ | |
4 | 2cn 11091 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 9994 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10048 | . . 3 ⊢ ((4 + 2) + 1) = (4 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2647 | . 2 ⊢ (4 + 3) = ((4 + 2) + 1) |
8 | df-7 11084 | . . 3 ⊢ 7 = (6 + 1) | |
9 | 4p2e6 11162 | . . . 4 ⊢ (4 + 2) = 6 | |
10 | 9 | oveq1i 6660 | . . 3 ⊢ ((4 + 2) + 1) = (6 + 1) |
11 | 8, 10 | eqtr4i 2647 | . 2 ⊢ 7 = ((4 + 2) + 1) |
12 | 7, 11 | eqtr4i 2647 | 1 ⊢ (4 + 3) = 7 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 1c1 9937 + caddc 9939 2c2 11070 3c3 11071 4c4 11072 6c6 11074 7c7 11075 |
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 |
This theorem is referenced by: 4p4e8 11164 37prm 15828 317prm 15833 1259lem5 15842 2503lem2 15845 4001lem1 15848 4001lem2 15849 log2ub 24676 bposlem8 25016 2lgslem3d 25124 2lgsoddprmlem3d 25138 hgt750lem 30729 hgt750lem2 30730 fmtno5lem4 41468 257prm 41473 127prm 41515 gbpart7 41655 sbgoldbwt 41665 sbgoldbst 41666 |
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