![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > tsetndxnbasendx | GIF version |
Description: The slot for the topology is not the slot for the base set in an extensible structure. (Contributed by AV, 21-Oct-2024.) (Proof shortened by AV, 31-Oct-2024.) |
Ref | Expression |
---|---|
tsetndxnbasendx | ⊢ (TopSet‘ndx) ≠ (Base‘ndx) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | basendxnn 12648 | . . 3 ⊢ (Base‘ndx) ∈ ℕ | |
2 | 1 | nnrei 8977 | . 2 ⊢ (Base‘ndx) ∈ ℝ |
3 | basendxlttsetndx 12781 | . 2 ⊢ (Base‘ndx) < (TopSet‘ndx) | |
4 | 2, 3 | gtneii 8101 | 1 ⊢ (TopSet‘ndx) ≠ (Base‘ndx) |
Colors of variables: wff set class |
Syntax hints: ≠ wne 2360 ‘cfv 5242 ndxcnx 12589 Basecbs 12592 TopSetcts 12675 |
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-in1 615 ax-in2 616 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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4143 ax-pow 4199 ax-pr 4234 ax-un 4458 ax-setind 4561 ax-cnex 7949 ax-resscn 7950 ax-1cn 7951 ax-1re 7952 ax-icn 7953 ax-addcl 7954 ax-addrcl 7955 ax-mulcl 7956 ax-addcom 7958 ax-addass 7960 ax-i2m1 7963 ax-0lt1 7964 ax-0id 7966 ax-rnegex 7967 ax-pre-ltirr 7970 ax-pre-lttrn 7972 ax-pre-ltadd 7974 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2758 df-sbc 2982 df-dif 3151 df-un 3153 df-in 3155 df-ss 3162 df-pw 3599 df-sn 3620 df-pr 3621 df-op 3623 df-uni 3832 df-int 3867 df-br 4026 df-opab 4087 df-mpt 4088 df-id 4318 df-xp 4657 df-rel 4658 df-cnv 4659 df-co 4660 df-dm 4661 df-rn 4662 df-res 4663 df-iota 5203 df-fun 5244 df-fv 5250 df-ov 5909 df-pnf 8042 df-mnf 8043 df-ltxr 8045 df-inn 8969 df-2 9027 df-3 9028 df-4 9029 df-5 9030 df-6 9031 df-7 9032 df-8 9033 df-9 9034 df-ndx 12595 df-slot 12596 df-base 12598 df-tset 12688 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |