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Mirrors > Home > MPE Home > Th. List > pnfnre2 | Structured version Visualization version GIF version |
Description: Plus infinity is not a real number. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
pnfnre2 | ⊢ ¬ +∞ ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfnre 10685 | . 2 ⊢ +∞ ∉ ℝ | |
2 | 1 | neli 3128 | 1 ⊢ ¬ +∞ ∈ ℝ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2113 ℝcr 10539 +∞cpnf 10675 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2796 ax-sep 5206 ax-nul 5213 ax-pr 5333 ax-un 7464 ax-resscn 10597 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2966 df-nel 3127 df-rab 3150 df-v 3499 df-dif 3942 df-un 3944 df-in 3946 df-ss 3955 df-nul 4295 df-pw 4544 df-sn 4571 df-pr 4573 df-uni 4842 df-pnf 10680 |
This theorem is referenced by: nn0xmulclb 30499 |
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