Theorem csbconstg 2983

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 2982 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 2255	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 2982	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1314   ∈ wcel 1463  ⦋csb 2971

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097

This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-v 2659  df-sbc 2879  df-csb 2972

This theorem is referenced by:  sbcel1g  2988  sbceq1g  2989  sbcel2g  2990  sbceq2g  2991  csbidmg  3022  sbcbr12g  3945  sbcbr1g  3946  sbcbr2g  3947  sbcrel  4585  csbcnvg  4683  csbresg  4780  sbcfung  5105  csbfv12g  5411  csbfv2g  5412  elfvmptrab  5470  csbov12g  5764  csbov1g  5765  csbov2g  5766