Theorem csbconstg 3151

Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 3150 with distinct variable requirement. (Contributed by Alan Sare, 22-Jul-2012.)

Assertion

Ref	Expression
csbconstg	⊢ (A ∈ V → [A / x]B = B)

Distinct variable group:   x,B

Allowed substitution hints:   A(x)   V(x)

Proof of Theorem csbconstg

Step	Hyp	Ref	Expression
1		nfcv 2490	. 2 ⊢ ℲxB
2	1	csbconstgf 3150	1 ⊢ (A ∈ V → [A / x]B = B)

Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  [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-or 359  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-v 2862  df-sbc 3048  df-csb 3138

This theorem is referenced by:  sbcel1g  3156  sbceq1g  3157  sbcel2g  3158  sbceq2g  3159  csbidmg  3191  sbcbr12g  4687  sbcbr1g  4688  sbcbr2g  4689  csbresg  4977  csbfv12g  5337  csbfv2g  5338  csbov12g  5554  csbov1g  5555  csbov2g  5556