Metamath Proof Explorer


Theorem csbex

Description: The existence of proper substitution into a class. (Contributed by NM, 7-Aug-2007) (Proof shortened by Andrew Salmon, 29-Jun-2011) (Revised by NM, 17-Aug-2018)

Ref Expression
Hypothesis csbex.1
|- B e. _V
Assertion csbex
|- [_ A / x ]_ B e. _V

Proof

Step Hyp Ref Expression
1 csbex.1
 |-  B e. _V
2 csbexg
 |-  ( A. x B e. _V -> [_ A / x ]_ B e. _V )
3 2 1 mpg
 |-  [_ A / x ]_ B e. _V