Theorem nfsbc1v 3066

Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)

Assertion

Ref	Expression
nfsbc1v	⊢ Ⅎx[̣A / x]̣φ

Distinct variable group:   x,A

Allowed substitution hint:   φ(x)

Proof of Theorem nfsbc1v

Step	Hyp	Ref	Expression
1		nfcv 2490	. 2 ⊢ ℲxA
2	1	nfsbc1 3065	1 ⊢ Ⅎx[̣A / x]̣φ

Syntax hints:  Ⅎwnf 1544  [̣wsbc 3047

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-sbc 3048

This theorem is referenced by:  elrabsf  3085  cbvralcsf  3199