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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 2178 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2185 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1243 Ⅎwnf 1349 Ⅎwnfc 2165 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 |
This theorem is referenced by: issetf 2562 eqvincf 2669 csbhypf 2885 nfpr 3420 intab 3644 nfmpt 3849 cbvmpt 3851 repizf2 3915 moop2 3988 eusvnf 4185 elrnmpt1 4585 fmptco 5330 elabrex 5397 nfmpt2 5573 cbvmpt2x 5582 ovmpt2dxf 5626 fmpt2x 5826 nfrecs 5922 erovlem 6198 nfsum1 9875 nfsum 9876 |
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