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Theorem nfrel 5238
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 5150 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2793 . . 3 𝑥(V × V)
42, 3nfss 3629 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1819 1 𝑥Rel 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnf 1748  wnfc 2780  Vcvv 3231  wss 3607   × cxp 5141  Rel wrel 5148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-in 3614  df-ss 3621  df-rel 5150
This theorem is referenced by:  nffun  5949
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