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Mirrors > Home > ILE Home > Th. List > xnegmnf | Unicode version |
Description: Minus . Remark of [BourbakiTop1] p. IV.15. (Contributed by FL, 26-Dec-2011.) (Revised by Mario Carneiro, 20-Aug-2015.) |
Ref | Expression |
---|---|
xnegmnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xneg 9722 | . 2 | |
2 | mnfnepnf 7968 | . . 3 | |
3 | ifnefalse 3536 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | eqid 2170 | . . 3 | |
6 | 5 | iftruei 3531 | . 2 |
7 | 1, 4, 6 | 3eqtri 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wne 2340 cif 3525 cpnf 7944 cmnf 7945 cneg 8084 cxne 9719 |
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-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-un 4416 ax-cnex 7858 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-nel 2436 df-rex 2454 df-rab 2457 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-if 3526 df-pw 3566 df-sn 3587 df-pr 3588 df-uni 3795 df-pnf 7949 df-mnf 7950 df-xr 7951 df-xneg 9722 |
This theorem is referenced by: xnegcl 9782 xnegneg 9783 xltnegi 9785 xnegid 9809 xnegdi 9818 xsubge0 9831 xposdif 9832 |
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