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Mirrors > Home > ILE Home > Th. List > pnfex | GIF version |
Description: Plus infinity exists (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
pnfex | ⊢ +∞ ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfxr 7942 | . 2 ⊢ +∞ ∈ ℝ* | |
2 | 1 | elexi 2733 | 1 ⊢ +∞ ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2135 Vcvv 2721 +∞cpnf 7921 ℝ*cxr 7923 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-un 4405 ax-cnex 7835 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-uni 3784 df-pnf 7926 df-xr 7928 |
This theorem is referenced by: mnfxr 7946 elxnn0 9170 elxr 9703 fxnn0nninf 10363 pc0 12213 |
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