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Mirrors > Home > ILE Home > Th. List > readdcli | GIF version |
Description: Closure law for addition of reals. (Contributed by NM, 17-Jan-1997.) |
Ref | Expression |
---|---|
recni.1 | ⊢ 𝐴 ∈ ℝ |
axri.2 | ⊢ 𝐵 ∈ ℝ |
Ref | Expression |
---|---|
readdcli | ⊢ (𝐴 + 𝐵) ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recni.1 | . 2 ⊢ 𝐴 ∈ ℝ | |
2 | axri.2 | . 2 ⊢ 𝐵 ∈ ℝ | |
3 | readdcl 7936 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ) | |
4 | 1, 2, 3 | mp2an 426 | 1 ⊢ (𝐴 + 𝐵) ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 (class class class)co 5874 ℝcr 7809 + caddc 7813 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 108 ax-addrcl 7907 |
This theorem is referenced by: resubcli 8218 eqneg 8687 2re 8987 3re 8991 4re 8994 5re 8996 6re 8998 7re 9000 8re 9002 9re 9004 numltc 9407 ef01bndlem 11759 ex-fl 14397 |
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