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Mirrors > Home > ILE Home > Th. List > 0cnALT | Unicode version |
Description: Alternate proof of 0cn 7751. (Contributed by NM, 19-Feb-2005.) (Revised by Mario Carneiro, 27-May-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
0cnALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-icn 7708 | . . 3 | |
2 | cnegex 7933 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | addcl 7738 | . . . . 5 | |
5 | 1, 4 | mpan 420 | . . . 4 |
6 | eleq1 2200 | . . . 4 | |
7 | 5, 6 | syl5ibcom 154 | . . 3 |
8 | 7 | rexlimiv 2541 | . 2 |
9 | 3, 8 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 wrex 2415 (class class class)co 5767 cc 7611 cc0 7613 ci 7615 caddc 7616 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-resscn 7705 ax-1cn 7706 ax-icn 7708 ax-addcl 7709 ax-addrcl 7710 ax-mulcl 7711 ax-addcom 7713 ax-addass 7715 ax-distr 7717 ax-i2m1 7718 ax-0id 7721 ax-rnegex 7722 ax-cnre 7724 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: (None) |
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