Theorem csbconstg 3072

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3071 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 2319	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3071	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1353   ∈ wcel 2148  ⦋csb 3058

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-sbc 2964  df-csb 3059

This theorem is referenced by:  sbcel1g  3077  sbceq1g  3078  sbcel2g  3079  sbceq2g  3080  csbidmg  3114  sbcbr12g  4059  sbcbr1g  4060  sbcbr2g  4061  sbcrel  4713  csbcnvg  4812  csbresg  4911  sbcfung  5241  csbfv12g  5552  csbfv2g  5553  elfvmptrab  5612  csbov12g  5914  csbov1g  5915  csbov2g  5916