Metamath Proof Explorer


Theorem nfan

Description: If x is not free in ph and ps , then it is not free in ( ph /\ ps ) . (Contributed by Mario Carneiro, 11-Aug-2016) (Proof shortened by Wolf Lammen, 13-Jan-2018) (Proof shortened by Wolf Lammen, 9-Oct-2021)

Ref Expression
Hypotheses nfan.1 x φ
nfan.2 x ψ
Assertion nfan x φ ψ

Proof

Step Hyp Ref Expression
1 nfan.1 x φ
2 nfan.2 x ψ
3 1 a1i x φ
4 2 a1i x ψ
5 3 4 nfand x φ ψ
6 5 mptru x φ ψ