Theorem csbvargi 33921

Description: The proper substitution of a class for a variable in that variable results in the class (if the class exists), in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.)

Hypothesis

Ref	Expression
csbvargi.1	|- A e. _V

Assertion

Ref	Expression
csbvargi	|- [_ A / x ]_ x = A

Proof of Theorem csbvargi

Step	Hyp	Ref	Expression
1		csbvargi.1	. 2 |- A e. _V
2		csbvarg 4003	. 2 |- ( A e. _V -> [_ A / x ]_ x = A )
3	1, 2	ax-mp 5	1 |- [_ A / x ]_ x = A

Syntax hints:   = wceq 1483   e. wcel 1990   _Vcvv 3200   [_csb 3533

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202  df-sbc 3436  df-csb 3534

This theorem is referenced by: (None)