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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 2319 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfel 2328 | 1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1460 ∈ wcel 2148 Ⅎwnfc 2306 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-cleq 2170 df-clel 2173 df-nfc 2308 |
This theorem is referenced by: vtocl2gf 2799 vtocl3gf 2800 vtoclgaf 2802 vtocl2gaf 2804 vtocl3gaf 2806 nfop 3794 pofun 4311 nfse 4340 rabxfrd 4468 mptfvex 5600 fvmptf 5607 fmptcof 5682 fliftfuns 5796 riota2f 5849 ovmpos 5995 ov2gf 5996 fmpox 6198 mpofvex 6201 qliftfuns 6616 xpf1o 6841 iunfidisj 6942 cc3 7264 sumfct 11375 sumrbdclem 11378 summodclem3 11381 summodclem2a 11382 zsumdc 11385 fsumgcl 11387 fsum3 11388 isumss 11392 isumss2 11394 fsum3cvg2 11395 fsumsplitf 11409 fsum2dlemstep 11435 fisumcom2 11439 fsumshftm 11446 fisum0diag2 11448 fsummulc2 11449 fsum00 11463 fsumabs 11466 fsumrelem 11472 fsumiun 11478 isumshft 11491 mertenslem2 11537 prodrbdclem 11572 prodmodclem3 11576 prodmodclem2a 11577 zproddc 11580 fprodseq 11584 prodfct 11588 prodssdc 11590 fprodmul 11592 fprodm1s 11602 fprodp1s 11603 fprodcl2lem 11606 fprodabs 11617 fprod2dlemstep 11623 fprodcom2fi 11627 fprodrec 11630 fproddivapf 11632 fprodsplitf 11633 fprodsplit1f 11635 fprodle 11641 infssuzcldc 11944 pcmpt 12333 pcmptdvds 12335 iuncld 13486 fsumcncntop 13927 |
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