![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 4re | GIF version |
Description: The number 4 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
4re | ⊢ 4 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 8978 | . 2 ⊢ 4 = (3 + 1) | |
2 | 3re 8991 | . . 3 ⊢ 3 ∈ ℝ | |
3 | 1re 7955 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7969 | . 2 ⊢ (3 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2250 | 1 ⊢ 4 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 (class class class)co 5874 ℝcr 7809 1c1 7811 + caddc 7813 3c3 8969 4c4 8970 |
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-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 ax-ext 2159 ax-1re 7904 ax-addrcl 7907 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-clel 2173 df-2 8976 df-3 8977 df-4 8978 |
This theorem is referenced by: 4cn 8995 5re 8996 4ne0 9015 4ap0 9016 5pos 9017 2lt4 9090 1lt4 9091 4lt5 9092 3lt5 9093 2lt5 9094 1lt5 9095 4lt6 9097 3lt6 9098 4lt7 9103 3lt7 9104 4lt8 9110 3lt8 9111 4lt9 9118 3lt9 9119 8th4div3 9136 div4p1lem1div2 9170 4lt10 9517 3lt10 9518 eluz4eluz2 9565 fz0to4untppr 10121 fzo0to42pr 10217 fldiv4p1lem1div2 10302 faclbnd2 10717 4bc2eq6 10749 resqrexlemover 11014 resqrexlemcalc1 11018 resqrexlemcalc2 11019 resqrexlemcalc3 11020 resqrexlemnm 11022 resqrexlemga 11027 sqrt2gt1lt2 11053 amgm2 11122 ef01bndlem 11759 sin01bnd 11760 cos01bnd 11761 cos2bnd 11763 flodddiv4 11933 tsetndxnstarvndx 12643 slotsdifplendx 12659 slotsdifdsndx 12670 slotsdifunifndx 12677 cnfldstr 13388 dveflem 14118 sin0pilem2 14134 sinhalfpilem 14143 sincosq1lem 14177 coseq0negpitopi 14188 tangtx 14190 sincos4thpi 14192 pigt3 14196 |
Copyright terms: Public domain | W3C validator |