Metamath Proof Explorer


Theorem ceqsal1t

Description: One direction of ceqsalt is based on fewer assumptions and fewer axioms. It is at the same time the reverse direction of vtoclgft . Extracted from a proof of ceqsalt . (Contributed by Wolf Lammen, 25-Mar-2025)

Ref Expression
Assertion ceqsal1t x ψ x x = A φ ψ ψ x x = A φ

Proof

Step Hyp Ref Expression
1 biimpr φ ψ ψ φ
2 1 imim2i x = A φ ψ x = A ψ φ
3 2 com23 x = A φ ψ ψ x = A φ
4 3 alimi x x = A φ ψ x ψ x = A φ
5 19.21t x ψ x ψ x = A φ ψ x x = A φ
6 4 5 imbitrid x ψ x x = A φ ψ ψ x x = A φ
7 6 imp x ψ x x = A φ ψ ψ x x = A φ