Theorem csbeq2i 3163

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 10	. . 3 |- ( T. -> B = C)
3	2	csbeq2dv 3162	. 2 |- ( T. -> [_A / x]_B = [_A / x]_C)
4	3	trud 1323	1 |- [_A / x]_B = [_A / x]_C

Syntax hints:   T. wtru 1316   = wceq 1642  [_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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3048  df-csb 3138

This theorem is referenced by:  csbvarg  3164  csbnest1g  3189  csbsng  3786  csbunig  3900  csbxpg  4814  csbrng  4967  csbresg  4977  csbfv12g  5337