Metamath Proof Explorer


Theorem nfsbc1

Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993) (Revised by Mario Carneiro, 12-Oct-2016)

Ref Expression
Hypothesis nfsbc1.1 _xA
Assertion nfsbc1 x[˙A/x]˙φ

Proof

Step Hyp Ref Expression
1 nfsbc1.1 _xA
2 1 a1i _xA
3 2 nfsbc1d x[˙A/x]˙φ
4 3 mptru x[˙A/x]˙φ