![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > nfel1 | GIF version |
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq1.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfel1 | ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeq1.1 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfcv 2282 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfel 2291 | 1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1437 ∈ wcel 1481 Ⅎwnfc 2269 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-cleq 2133 df-clel 2136 df-nfc 2271 |
This theorem is referenced by: vtocl2gf 2751 vtocl3gf 2752 vtoclgaf 2754 vtocl2gaf 2756 vtocl3gaf 2758 nfop 3729 pofun 4242 nfse 4271 rabxfrd 4398 mptfvex 5514 fvmptf 5521 fmptcof 5595 fliftfuns 5707 riota2f 5759 ovmpos 5902 ov2gf 5903 fmpox 6106 mpofvex 6109 qliftfuns 6521 xpf1o 6746 iunfidisj 6842 cc3 7100 sumfct 11175 sumrbdclem 11178 summodclem3 11181 summodclem2a 11182 zsumdc 11185 fsumgcl 11187 fsum3 11188 isumss 11192 isumss2 11194 fsum3cvg2 11195 fsumsplitf 11209 fsum2dlemstep 11235 fisumcom2 11239 fsumshftm 11246 fisum0diag2 11248 fsummulc2 11249 fsum00 11263 fsumabs 11266 fsumrelem 11272 fsumiun 11278 isumshft 11291 mertenslem2 11337 prodrbdclem 11372 prodmodclem3 11376 prodmodclem2a 11377 zproddc 11380 fprodseq 11384 infssuzcldc 11680 iuncld 12323 fsumcncntop 12764 |
Copyright terms: Public domain | W3C validator |