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Mirrors > Home > ILE Home > Th. List > reelprrecn | GIF version |
Description: Reals are a subset of the pair of real and complex numbers (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
reelprrecn | ⊢ ℝ ∈ {ℝ, ℂ} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reex 7975 | . 2 ⊢ ℝ ∈ V | |
2 | 1 | prid1 3713 | 1 ⊢ ℝ ∈ {ℝ, ℂ} |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 {cpr 3608 ℂcc 7839 ℝcr 7840 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7932 ax-resscn 7933 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 |
This theorem is referenced by: dvfpm 14618 dvmptcjx 14646 |
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