Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > 7p3e10OLD | Structured version Visualization version GIF version |
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 7p3e10 11603 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
7p3e10OLD | ⊢ (7 + 3) = 10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 11080 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 6661 | . . 3 ⊢ (7 + 3) = (7 + (2 + 1)) |
3 | 7cn 11104 | . . . 4 ⊢ 7 ∈ ℂ | |
4 | 2cn 11091 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 9994 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10048 | . . 3 ⊢ ((7 + 2) + 1) = (7 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2647 | . 2 ⊢ (7 + 3) = ((7 + 2) + 1) |
8 | df-10OLD 11087 | . . 3 ⊢ 10 = (9 + 1) | |
9 | 7p2e9 11172 | . . . 4 ⊢ (7 + 2) = 9 | |
10 | 9 | oveq1i 6660 | . . 3 ⊢ ((7 + 2) + 1) = (9 + 1) |
11 | 8, 10 | eqtr4i 2647 | . 2 ⊢ 10 = ((7 + 2) + 1) |
12 | 7, 11 | eqtr4i 2647 | 1 ⊢ (7 + 3) = 10 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 1c1 9937 + caddc 9939 2c2 11070 3c3 11071 7c7 11075 9c9 11077 10c10 11078 |
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 df-10OLD 11087 |
This theorem is referenced by: 7p3e10bOLD 11604 7p4e11OLD 11606 |
Copyright terms: Public domain | W3C validator |