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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 )