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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 7973 | . . 3 | |
2 | 1 | oveq2i 5523 | . 2 |
3 | df-4 7975 | . . 3 | |
4 | df-3 7974 | . . . 4 | |
5 | 4 | oveq1i 5522 | . . 3 |
6 | 2cn 7986 | . . . 4 | |
7 | ax-1cn 6977 | . . . 4 | |
8 | 6, 7, 7 | addassi 7035 | . . 3 |
9 | 3, 5, 8 | 3eqtri 2064 | . 2 |
10 | 2, 9 | eqtr4i 2063 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 (class class class)co 5512 c1 6890 caddc 6892 c2 7964 c3 7965 c4 7966 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-resscn 6976 ax-1cn 6977 ax-1re 6978 ax-addrcl 6981 ax-addass 6986 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 df-2 7973 df-3 7974 df-4 7975 |
This theorem is referenced by: 2t2e4 8069 i4 9355 resqrexlemover 9608 resqrexlemcalc1 9612 |
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