Theorem csbeq2i 2870

Description: Formula-building inference rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)

Hypothesis

Ref	Expression
csbeq2i.1	⊢ B = 𝐶

Assertion

Ref	Expression
csbeq2i	⊢ ⦋A / x⦌B = ⦋A / x⦌𝐶

Proof of Theorem csbeq2i

Step	Hyp	Ref	Expression
1		csbeq2i.1	. . . 4 ⊢ B = 𝐶
2	1	a1i 9	. . 3 ⊢ ( ⊤ → B = 𝐶)
3	2	csbeq2dv 2869	. 2 ⊢ ( ⊤ → ⦋A / x⦌B = ⦋A / x⦌𝐶)
4	3	trud 1251	1 ⊢ ⦋A / x⦌B = ⦋A / x⦌𝐶

Syntax hints:   = wceq 1242   ⊤ wtru 1243  ⦋csb 2846

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759  df-csb 2847

This theorem is referenced by:  csbvarg  2871  csbnest1g  2895  csbsng  3422  csbunig  3579  csbxpg  4364  csbcnvg  4462  csbdmg  4472  csbresg  4558  csbrng  4725  csbfv12g  5152  csbnegg  6986