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Mirrors > Home > ILE Home > Th. List > 5p4e9 | Unicode version |
Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
5p4e9 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 8956 |
. . . 4
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2 | 1 | oveq2i 5879 |
. . 3
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3 | 5cn 8975 |
. . . 4
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4 | 3cn 8970 |
. . . 4
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5 | ax-1cn 7882 |
. . . 4
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6 | 3, 4, 5 | addassi 7943 |
. . 3
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7 | 2, 6 | eqtr4i 2201 |
. 2
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8 | df-9 8961 |
. . 3
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9 | 5p3e8 9042 |
. . . 4
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10 | 9 | oveq1i 5878 |
. . 3
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11 | 8, 10 | eqtr4i 2201 |
. 2
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12 | 7, 11 | eqtr4i 2201 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-resscn 7881 ax-1cn 7882 ax-1re 7883 ax-addrcl 7886 ax-addass 7891 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-iota 5173 df-fv 5219 df-ov 5871 df-2 8954 df-3 8955 df-4 8956 df-5 8957 df-6 8958 df-7 8959 df-8 8960 df-9 8961 |
This theorem is referenced by: 5p5e10 9430 |
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