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Mirrors > Home > MPE Home > Th. List > 6p4e10OLD | Structured version Visualization version GIF version |
Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 6p4e10 11474 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
6p4e10OLD | ⊢ (6 + 4) = 10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 10958 | . . . 4 ⊢ 4 = (3 + 1) | |
2 | 1 | oveq2i 6560 | . . 3 ⊢ (6 + 4) = (6 + (3 + 1)) |
3 | 6cn 10979 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 3cn 10972 | . . . 4 ⊢ 3 ∈ ℂ | |
5 | ax-1cn 9873 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 9927 | . . 3 ⊢ ((6 + 3) + 1) = (6 + (3 + 1)) |
7 | 2, 6 | eqtr4i 2635 | . 2 ⊢ (6 + 4) = ((6 + 3) + 1) |
8 | df-10OLD 10964 | . . 3 ⊢ 10 = (9 + 1) | |
9 | 6p3e9 11047 | . . . 4 ⊢ (6 + 3) = 9 | |
10 | 9 | oveq1i 6559 | . . 3 ⊢ ((6 + 3) + 1) = (9 + 1) |
11 | 8, 10 | eqtr4i 2635 | . 2 ⊢ 10 = ((6 + 3) + 1) |
12 | 7, 11 | eqtr4i 2635 | 1 ⊢ (6 + 4) = 10 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 (class class class)co 6549 1c1 9816 + caddc 9818 3c3 10948 4c4 10949 6c6 10951 9c9 10954 10c10 10955 |
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 df-6 10960 df-7 10961 df-8 10962 df-9 10963 df-10OLD 10964 |
This theorem is referenced by: 6p4e10bOLD 11475 6p5e11OLD 11477 6t5e30OLD 11521 |
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