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Mirrors > Home > ILE Home > Th. List > 0cnALT | Unicode version |
Description: Alternate proof of 0cn 7946. (Contributed by NM, 19-Feb-2005.) (Revised by Mario Carneiro, 27-May-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
0cnALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-icn 7903 |
. . 3
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2 | cnegex 8131 |
. . 3
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3 | 1, 2 | ax-mp 5 |
. 2
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4 | addcl 7933 |
. . . . 5
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5 | 1, 4 | mpan 424 |
. . . 4
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6 | eleq1 2240 |
. . . 4
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7 | 5, 6 | syl5ibcom 155 |
. . 3
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8 | 7 | rexlimiv 2588 |
. 2
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9 | 3, 8 | ax-mp 5 |
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 7900 ax-1cn 7901 ax-icn 7903 ax-addcl 7904 ax-addrcl 7905 ax-mulcl 7906 ax-addcom 7908 ax-addass 7910 ax-distr 7912 ax-i2m1 7913 ax-0id 7916 ax-rnegex 7917 ax-cnre 7919 |
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-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-iota 5177 df-fv 5223 df-ov 5875 |
This theorem is referenced by: (None) |
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