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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 8637 |
. . 3
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2 | 1 | oveq2i 5717 |
. 2
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3 | df-4 8639 |
. . 3
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4 | df-3 8638 |
. . . 4
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5 | 4 | oveq1i 5716 |
. . 3
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6 | 2cn 8649 |
. . . 4
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7 | ax-1cn 7588 |
. . . 4
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8 | 6, 7, 7 | addassi 7646 |
. . 3
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9 | 3, 5, 8 | 3eqtri 2124 |
. 2
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10 | 2, 9 | eqtr4i 2123 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-resscn 7587 ax-1cn 7588 ax-1re 7589 ax-addrcl 7592 ax-addass 7597 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-iota 5024 df-fv 5067 df-ov 5709 df-2 8637 df-3 8638 df-4 8639 |
This theorem is referenced by: 2t2e4 8726 i4 10236 4bc2eq6 10361 resqrexlemover 10622 resqrexlemcalc1 10626 ef01bndlem 11261 6gcd4e2 11476 |
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