Theorem nfcsb1v 3169

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by NM, 17-Aug-2006.) (Revised by Mario Carneiro, 12-Oct-2016.)

Assertion

Ref	Expression
nfcsb1v	⊢ Ⅎx[A / x]B

Distinct variable group:   x,A

Allowed substitution hint:   B(x)

Proof of Theorem nfcsb1v

Step	Hyp	Ref	Expression
1		nfcv 2490	. 2 ⊢ ℲxA
2	1	nfcsb1 3168	1 ⊢ Ⅎx[A / x]B

Syntax hints:  Ⅎwnfc 2477  [csb 3137

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  df-csb 3138

This theorem is referenced by:  csbhypf  3172  csbiebt  3173  sbcnestgf  3184  csbnest1g  3189  cbvralcsf  3199  cbvreucsf  3201  cbvrabcsf  3202  csbing  3463  csbifg  3691  sbcbrg  4686  opeliunxp  4821  csbima12g  4956  csbovg  5553  fvmpts  5702  fvmpt2i  5704  fvmptex  5722  fmpt2x  5731