Metamath Proof Explorer


Theorem wdomimag

Description: A set is weakly dominant over its image under any function. (Contributed by Stefan O'Rear, 14-Feb-2015) (Revised by Mario Carneiro, 25-Jun-2015)

Ref Expression
Assertion wdomimag ⊢ Fun ⁡ F ∧ A ∈ V → F A ≼ * A

Proof

Step Hyp Ref Expression
1 funimaexg ⊢ Fun ⁡ F ∧ A ∈ V → F A ∈ V
2 wdomima2g ⊢ Fun ⁡ F ∧ A ∈ V ∧ F A ∈ V → F A ≼ * A
3 1 2 mpd3an3 ⊢ Fun ⁡ F ∧ A ∈ V → F A ≼ * A