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Mirrors > Home > ILE Home > Th. List > nfeq1 | GIF version |
Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq1.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfeq1 | ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeq1.1 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfcv 2312 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2320 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 Ⅎwnf 1453 Ⅎwnfc 2299 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 |
This theorem is referenced by: euabsn 3653 fvmptt 5587 eusvobj2 5839 ovmpodv2 5986 ovi3 5989 dom2lem 6750 seq3f1olemstep 10457 seq3f1olemp 10458 fsumf1o 11353 isumss 11354 isummulc2 11389 fsum00 11425 isumshft 11453 fprodf1o 11551 prodssdc 11552 |
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