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Mirrors > Home > MPE Home > Th. List > ltpnfd | Structured version Visualization version GIF version |
Description: Any (finite) real is less than plus infinity. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
ltpnfd.a | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
Ref | Expression |
---|---|
ltpnfd | ⊢ (𝜑 → 𝐴 < +∞) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltpnfd.a | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
2 | ltpnf 12591 | . 2 ⊢ (𝐴 ∈ ℝ → 𝐴 < +∞) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 < +∞) |
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