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Theorem nfrel 4452
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 4379 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2194 . . 3 𝑥(V × V)
42, 3nfss 2965 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1379 1 𝑥Rel 𝐴
Colors of variables: wff set class
Syntax hints:  wnf 1365  wnfc 2181  Vcvv 2574  wss 2944   × cxp 4370  Rel wrel 4377
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-in 2951  df-ss 2958  df-rel 4379
This theorem is referenced by:  nffun  4951
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