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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 7939 | . 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 5877 ℝcr 7812 + caddc 7816 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 108 ax-addrcl 7910 |
This theorem is referenced by: resubcli 8222 eqneg 8691 2re 8991 3re 8995 4re 8998 5re 9000 6re 9002 7re 9004 8re 9006 9re 9008 numltc 9411 ef01bndlem 11766 ex-fl 14562 |
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