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Theorem nfrel 5641
 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 5549 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2982 . . 3 𝑥(V × V)
42, 3nfss 3945 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1854 1 𝑥Rel 𝐴
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1785  Ⅎwnfc 2962  Vcvv 3480   ⊆ wss 3919   × cxp 5540  Rel wrel 5547 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-v 3482  df-in 3926  df-ss 3936  df-rel 5549 This theorem is referenced by:  nffun  6366
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