Metamath Proof Explorer


Theorem ineccnvmo2

Description: Equivalence of a double universal quantification restricted to the range and an "at most one" inside a universal quantification. (Contributed by Peter Mazsa, 4-Sep-2021)

Ref Expression
Assertion ineccnvmo2 x ran F y ran F x = y x F -1 y F -1 = u * x u F x

Proof

Step Hyp Ref Expression
1 ineccnvmo x ran F y ran F x = y x F -1 y F -1 = u * x ran F u F x
2 alrmomorn u * x ran F u F x u * x u F x
3 1 2 bitri x ran F y ran F x = y x F -1 y F -1 = u * x u F x