Theorem csbconstgf 3150

Description: Substitution doesn't affect a constant B (in which x is not free). (Contributed by NM, 10-Nov-2005.)

Hypothesis

Ref	Expression
csbconstgf.1	⊢ ℲxB

Assertion

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

Proof of Theorem csbconstgf

Step	Hyp	Ref	Expression
1		csbconstgf.1	. 2 ⊢ ℲxB
2		csbtt 3149	. 2 ⊢ ((A ∈ V ∧ ℲxB) → [A / x]B = B)
3	1, 2	mpan2 652	1 ⊢ (A ∈ V → [A / x]B = B)

Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  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-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:  csbconstg  3151