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Mirrors > Home > ILE Home > Th. List > 2cnd | GIF version |
Description: 2 is a complex number, deductive form (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
2cnd | ⊢ (𝜑 → 2 ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 7986 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | a1i 9 | 1 ⊢ (𝜑 → 2 ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1393 ℂcc 6887 2c2 7964 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-resscn 6976 ax-1re 6978 ax-addrcl 6981 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-in 2924 df-ss 2931 df-2 7973 |
This theorem is referenced by: cnm2m1cnm3 8176 nneo 8341 zeo2 8344 2tnp1ge0ge0 9143 flhalf 9144 binom3 9366 zesq 9367 cvg1nlemcxze 9581 resqrexlemover 9608 resqrexlemlo 9611 resqrexlemcalc1 9612 resqrexlemnm 9616 amgm2 9714 sqr2irrlem 9877 sqrt2irr 9878 |
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