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Mirrors > Home > ILE Home > Th. List > 8p2e10 | Unicode version |
Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
8p2e10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 9009 |
. . . 4
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2 | 1 | oveq2i 5908 |
. . 3
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3 | 8cn 9036 |
. . . 4
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4 | ax-1cn 7935 |
. . . 4
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5 | 3, 4, 4 | addassi 7996 |
. . 3
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6 | 2, 5 | eqtr4i 2213 |
. 2
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7 | df-9 9016 |
. . 3
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8 | 7 | oveq1i 5907 |
. 2
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9 | 9p1e10 9417 |
. 2
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10 | 6, 8, 9 | 3eqtr2i 2216 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7933 ax-resscn 7934 ax-1cn 7935 ax-1re 7936 ax-icn 7937 ax-addcl 7938 ax-addrcl 7939 ax-mulcl 7940 ax-mulcom 7943 ax-addass 7944 ax-mulass 7945 ax-distr 7946 ax-1rid 7949 ax-0id 7950 ax-cnre 7953 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5900 df-inn 8951 df-2 9009 df-3 9010 df-4 9011 df-5 9012 df-6 9013 df-7 9014 df-8 9015 df-9 9016 df-dec 9416 |
This theorem is referenced by: 8p3e11 9495 8t5e40 9532 |
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