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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 2175 | . 2 ⊢ ℲxA | |
2 | nfeq2.1 | . 2 ⊢ ℲxB | |
3 | 1, 2 | nfeq 2182 | 1 ⊢ Ⅎx A = B |
Colors of variables: wff set class |
Syntax hints: = wceq 1242 Ⅎwnf 1346 Ⅎwnfc 2162 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-cleq 2030 df-clel 2033 df-nfc 2164 |
This theorem is referenced by: issetf 2556 eqvincf 2663 csbhypf 2879 nfpr 3411 intab 3635 nfmpt 3840 cbvmpt 3842 repizf2 3906 moop2 3979 eusvnf 4151 elrnmpt1 4528 fmptco 5273 elabrex 5340 nfmpt2 5515 cbvmpt2x 5524 ovmpt2dxf 5568 fmpt2x 5768 nfrecs 5863 erovlem 6134 |
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