Metamath Proof Explorer


Theorem qliftrel

Description: F , a function lift, is a subset of R X. S . (Contributed by Mario Carneiro, 23-Dec-2016) (Revised by AV, 3-Aug-2024)

Ref Expression
Hypotheses qlift.1 F = ran x X x R A
qlift.2 φ x X A Y
qlift.3 φ R Er X
qlift.4 φ X V
Assertion qliftrel φ F X / R × Y

Proof

Step Hyp Ref Expression
1 qlift.1 F = ran x X x R A
2 qlift.2 φ x X A Y
3 qlift.3 φ R Er X
4 qlift.4 φ X V
5 1 2 3 4 qliftlem φ x X x R X / R
6 1 5 2 fliftrel φ F X / R × Y