Metamath Proof Explorer

Theorem nfcsb1

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016)

Ref Expression
Hypothesis nfcsb1.1 
|- F/_ x A
Assertion nfcsb1 
|- F/_ x [_ A / x ]_ B

Proof

Step Hyp Ref Expression
1 nfcsb1.1 
 |-  F/_ x A
2 1 a1i 
 |-  ( T. -> F/_ x A )
3 2 nfcsb1d 
 |-  ( T. -> F/_ x [_ A / x ]_ B )
4 3 mptru 
 |-  F/_ x [_ A / x ]_ B