Metamath Proof Explorer

Theorem 19.41v

Description: Version of 19.41 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993) Remove dependency on ax-6 . (Revised by Rohan Ridenour, 15-Apr-2022)

Ref Expression
Assertion 19.41v x φ ψ x φ ψ


Step Hyp Ref Expression
1 19.40 x φ ψ x φ x ψ
2 ax5e x ψ ψ
3 2 anim2i x φ x ψ x φ ψ
4 1 3 syl x φ ψ x φ ψ
5 pm3.21 ψ φ φ ψ
6 5 eximdv ψ x φ x φ ψ
7 6 impcom x φ ψ x φ ψ
8 4 7 impbii x φ ψ x φ ψ