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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 2347 | . 2 ⊢ Ⅎ𝑥𝐴 | |
| 2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
| 3 | 1, 2 | nfeq 2355 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
| Colors of variables: wff set class |
| Syntax hints: = wceq 1372 Ⅎwnf 1482 Ⅎwnfc 2334 |
| 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 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-cleq 2197 df-clel 2200 df-nfc 2336 |
| This theorem is referenced by: issetf 2778 eqvincf 2897 csbhypf 3131 nfpr 3682 intab 3913 nfmpt 4135 cbvmptf 4137 cbvmpt 4138 repizf2 4205 moop2 4295 eusvnf 4499 elrnmpt1 4928 iotaexab 5249 fmptco 5745 elabrex 5825 elabrexg 5826 nfmpo 6013 cbvmpox 6022 ovmpodxf 6070 fmpox 6285 f1od2 6320 nfrecs 6392 erovlem 6713 xpf1o 6940 mapxpen 6944 mkvprop 7259 cc3 7379 lble 9019 nfsum1 11609 nfsum 11610 zsumdc 11637 fsum3 11640 fsum3cvg2 11647 fsum2dlemstep 11687 mertenslem2 11789 nfcprod1 11807 nfcprod 11808 zproddc 11832 fprod2dlemstep 11875 ctiunctlemfo 12752 ellimc3apf 15074 |
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