Metamath Proof Explorer


Theorem nf3an

Description: If x is not free in ph , ps , and ch , then it is not free in ( ph /\ ps /\ ch ) . (Contributed by Mario Carneiro, 11-Aug-2016)

Ref Expression
Hypotheses nfan.1 x φ
nfan.2 x ψ
nfan.3 x χ
Assertion nf3an x φ ψ χ

Proof

Step Hyp Ref Expression
1 nfan.1 x φ
2 nfan.2 x ψ
3 nfan.3 x χ
4 df-3an φ ψ χ φ ψ χ
5 1 2 nfan x φ ψ
6 5 3 nfan x φ ψ χ
7 4 6 nfxfr x φ ψ χ