Metamath Proof Explorer


Theorem bj-nfimt

Description: Closed form of nfim and curried (exported) form of nfimt . (Contributed by BJ, 20-Oct-2021)

Ref Expression
Assertion bj-nfimt x φ x ψ x φ ψ

Proof

Step Hyp Ref Expression
1 19.35 x φ ψ x φ x ψ
2 id x φ x φ
3 2 nfrd x φ x φ x φ
4 3 imim1d x φ x φ x ψ x φ x ψ
5 1 4 syl5bi x φ x φ ψ x φ x ψ
6 id x ψ x ψ
7 6 nfrd x ψ x ψ x ψ
8 7 imim2d x ψ x φ x ψ x φ x ψ
9 19.38 x φ x ψ x φ ψ
10 8 9 syl6 x ψ x φ x ψ x φ ψ
11 5 10 syl9 x φ x ψ x φ ψ x φ ψ
12 df-nf x φ ψ x φ ψ x φ ψ
13 11 12 syl6ibr x φ x ψ x φ ψ