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Mirrors > Home > ILE Home > Th. List > 7p3e10 | Unicode version |
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
7p3e10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8872 |
. . . 4
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2 | 1 | oveq2i 5825 |
. . 3
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3 | 7cn 8896 |
. . . 4
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4 | 2cn 8883 |
. . . 4
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5 | ax-1cn 7804 |
. . . 4
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6 | 3, 4, 5 | addassi 7865 |
. . 3
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7 | 2, 6 | eqtr4i 2178 |
. 2
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8 | 7p2e9 8963 |
. . 3
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9 | 8 | oveq1i 5824 |
. 2
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10 | 9p1e10 9276 |
. 2
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11 | 7, 9, 10 | 3eqtri 2179 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-ext 2136 ax-sep 4078 ax-cnex 7802 ax-resscn 7803 ax-1cn 7804 ax-1re 7805 ax-icn 7806 ax-addcl 7807 ax-addrcl 7808 ax-mulcl 7809 ax-mulcom 7812 ax-addass 7813 ax-mulass 7814 ax-distr 7815 ax-1rid 7818 ax-0id 7819 ax-cnre 7822 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1740 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ral 2437 df-rex 2438 df-rab 2441 df-v 2711 df-un 3102 df-in 3104 df-ss 3111 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-int 3804 df-br 3962 df-iota 5128 df-fv 5171 df-ov 5817 df-inn 8813 df-2 8871 df-3 8872 df-4 8873 df-5 8874 df-6 8875 df-7 8876 df-8 8877 df-9 8878 df-dec 9275 |
This theorem is referenced by: 7p4e11 9349 |
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