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Mirrors > Home > ILE Home > Th. List > 2p2e4 | Unicode version |
Description: Two plus two equals four. For more information, see "2+2=4 Trivia" on the Metamath Proof Explorer Home Page: http://us.metamath.org/mpeuni/mmset.html#trivia. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
2p2e4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8098 | . . 3 | |
2 | 1 | oveq2i 5543 | . 2 |
3 | df-4 8100 | . . 3 | |
4 | df-3 8099 | . . . 4 | |
5 | 4 | oveq1i 5542 | . . 3 |
6 | 2cn 8110 | . . . 4 | |
7 | ax-1cn 7069 | . . . 4 | |
8 | 6, 7, 7 | addassi 7127 | . . 3 |
9 | 3, 5, 8 | 3eqtri 2105 | . 2 |
10 | 2, 9 | eqtr4i 2104 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 (class class class)co 5532 c1 6982 caddc 6984 c2 8089 c3 8090 c4 8091 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-resscn 7068 ax-1cn 7069 ax-1re 7070 ax-addrcl 7073 ax-addass 7078 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 df-2 8098 df-3 8099 df-4 8100 |
This theorem is referenced by: 2t2e4 8186 i4 9577 4bc2eq6 9701 resqrexlemover 9896 resqrexlemcalc1 9900 6gcd4e2 10384 |
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