Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2098
class class class wbr 5139 +∞cpnf 11244
ℝ*cxr 11246
≤ cle 11248 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-ext 2695 ax-sep 5290 ax-nul 5297 ax-pow 5354 ax-pr 5418 ax-un 7719 ax-cnex 11163 ax-resscn 11164 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-ne 2933 df-nel 3039 df-ral 3054 df-rex 3063 df-rab 3425 df-v 3468 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-nul 4316 df-if 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-br 5140 df-opab 5202 df-xp 5673 df-cnv 5675 df-pnf 11249 df-mnf 11250 df-xr 11251 df-ltxr 11252 df-le 11253 |
This theorem is referenced by: xlimpnfvlem2
45099 xlimliminflimsup
45124 pimgtpnf2f
45967 |