Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfeq2 | GIF version |
Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq2.1 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfeq2 | ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2312 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2320 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 Ⅎwnf 1453 Ⅎwnfc 2299 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 |
This theorem is referenced by: issetf 2737 eqvincf 2855 csbhypf 3087 nfpr 3633 intab 3860 nfmpt 4081 cbvmptf 4083 cbvmpt 4084 repizf2 4148 moop2 4236 eusvnf 4438 elrnmpt1 4862 fmptco 5662 elabrex 5737 nfmpo 5922 cbvmpox 5931 ovmpodxf 5978 fmpox 6179 f1od2 6214 nfrecs 6286 erovlem 6605 xpf1o 6822 mapxpen 6826 mkvprop 7134 cc3 7230 lble 8863 nfsum1 11319 nfsum 11320 zsumdc 11347 fsum3 11350 fsum3cvg2 11357 fsum2dlemstep 11397 mertenslem2 11499 nfcprod1 11517 nfcprod 11518 zproddc 11542 fprod2dlemstep 11585 ctiunctlemfo 12394 ellimc3apf 13423 |
Copyright terms: Public domain | W3C validator |