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Theorem nfrel 4592
 Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrel.1 𝑥𝐴
Assertion
Ref Expression
nfrel 𝑥Rel 𝐴

Proof of Theorem nfrel
StepHypRef Expression
1 df-rel 4514 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2256 . . 3 𝑥(V × V)
42, 3nfss 3058 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1433 1 𝑥Rel 𝐴
 Colors of variables: wff set class Syntax hints:  Ⅎwnf 1419  Ⅎwnfc 2243  Vcvv 2658   ⊆ wss 3039   × cxp 4505  Rel wrel 4512 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-in 3045  df-ss 3052  df-rel 4514 This theorem is referenced by:  nffun  5114
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