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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 2229 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2237 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1290 Ⅎwnf 1395 Ⅎwnfc 2216 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-cleq 2082 df-clel 2085 df-nfc 2218 |
This theorem is referenced by: issetf 2627 eqvincf 2743 csbhypf 2967 nfpr 3496 intab 3723 nfmpt 3936 cbvmptf 3938 cbvmpt 3939 repizf2 4003 moop2 4087 eusvnf 4288 elrnmpt1 4699 fmptco 5478 elabrex 5551 nfmpt2 5731 cbvmpt2x 5740 ovmpt2dxf 5784 fmpt2x 5984 f1od2 6014 nfrecs 6086 erovlem 6398 xpf1o 6614 mapxpen 6618 lble 8462 nfsum1 10799 nfsum 10800 zisum 10828 fisum 10832 fisumcvg2 10840 fsum3cvg2 10841 fsum2dlemstep 10882 mertenslem2 10984 |
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