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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: https://us.metamath.org/mpeuni/mmset.html#trivia. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
2p2e4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8992 |
. . 3
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2 | 1 | oveq2i 5899 |
. 2
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3 | df-4 8994 |
. . 3
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4 | df-3 8993 |
. . . 4
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5 | 4 | oveq1i 5898 |
. . 3
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6 | 2cn 9004 |
. . . 4
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7 | ax-1cn 7918 |
. . . 4
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8 | 6, 7, 7 | addassi 7979 |
. . 3
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9 | 3, 5, 8 | 3eqtri 2212 |
. 2
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10 | 2, 9 | eqtr4i 2211 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 ax-resscn 7917 ax-1cn 7918 ax-1re 7919 ax-addrcl 7922 ax-addass 7927 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-iota 5190 df-fv 5236 df-ov 5891 df-2 8992 df-3 8993 df-4 8994 |
This theorem is referenced by: 2t2e4 9087 i4 10637 4bc2eq6 10768 resqrexlemover 11033 resqrexlemcalc1 11037 ef01bndlem 11778 6gcd4e2 12010 pythagtriplem1 12279 |
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