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Theorem nfrel 5362
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 5274 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2903 . . 3 𝑥(V × V)
42, 3nfss 3738 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1928 1 𝑥Rel 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnf 1857  wnfc 2890  Vcvv 3341  wss 3716   × cxp 5265  Rel wrel 5272
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-ral 3056  df-in 3723  df-ss 3730  df-rel 5274
This theorem is referenced by:  nffun  6073
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