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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 2258 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2266 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 Ⅎwnf 1421 Ⅎwnfc 2245 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-cleq 2110 df-clel 2113 df-nfc 2247 |
This theorem is referenced by: issetf 2667 eqvincf 2784 csbhypf 3008 nfpr 3543 intab 3770 nfmpt 3990 cbvmptf 3992 cbvmpt 3993 repizf2 4056 moop2 4143 eusvnf 4344 elrnmpt1 4760 fmptco 5554 elabrex 5627 nfmpo 5808 cbvmpox 5817 ovmpodxf 5864 fmpox 6066 f1od2 6100 nfrecs 6172 erovlem 6489 xpf1o 6706 mapxpen 6710 mkvprop 7000 lble 8669 nfsum1 11080 nfsum 11081 zsumdc 11108 fsum3 11111 fsum3cvg2 11118 fsum2dlemstep 11158 mertenslem2 11260 ctiunctlemfo 11863 ellimc3apf 12709 |
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