Theorem intima0

Description: Two ways of expressing the intersection of images of a class. (Contributed by RP, 13-Apr-2020)

	Ref	Expression
Assertion	intima0	⊢ ∩ 𝑎 ∈ 𝐴 ( 𝑎 “ 𝐵 ) = ∩ { 𝑥 ∣ ∃ 𝑎 ∈ 𝐴 𝑥 = ( 𝑎 “ 𝐵 ) }

Proof

Step	Hyp	Ref	Expression
1		vex	⊢ 𝑎 ∈ V
2	1	imaex	⊢ ( 𝑎 “ 𝐵 ) ∈ V
3	2	dfiin2	⊢ ∩ 𝑎 ∈ 𝐴 ( 𝑎 “ 𝐵 ) = ∩ { 𝑥 ∣ ∃ 𝑎 ∈ 𝐴 𝑥 = ( 𝑎 “ 𝐵 ) }