Theorem nfrel 5764

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	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfrel	⊢ Ⅎ𝑥Rel 𝐴

Proof of Theorem nfrel

Step	Hyp	Ref	Expression
1		df-rel 5665	. 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V))
2		nfrel.1	. . 3 ⊢ Ⅎ𝑥𝐴
3		nfcv 2926	. . 3 ⊢ Ⅎ𝑥(V × V)
4	2, 3	nfss 3906	. 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V)
5	1, 4	nfxfr 1886	1 ⊢ Ⅎ𝑥Rel 𝐴

This proof depends on syntax axioms:  Ⅎwnf 1816  Ⅎwnfc 2911  Vcvv 3454   ⊆ wss 3900   × cxp 5656  Rel wrel 5663

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-10 2180  ax-11 2197  ax-12 2216

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817  df-clel 2839  df-nfc 2913  df-ral 3081  df-ss 3901  df-rel 5665

This theorem is used by:  nffun  6590