Theorem imadisjld

Description: Natural dduction form of one side of imadisj . (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypothesis	imadisjld.1	⊢ ( 𝜑 → ( dom 𝐴 ∩ 𝐵 ) = ∅ )
Assertion	imadisjld	⊢ ( 𝜑 → ( 𝐴 “ 𝐵 ) = ∅ )

Proof

Step	Hyp	Ref	Expression
1		imadisjld.1	⊢ ( 𝜑 → ( dom 𝐴 ∩ 𝐵 ) = ∅ )
2		imadisj	⊢ ( ( 𝐴 “ 𝐵 ) = ∅ ↔ ( dom 𝐴 ∩ 𝐵 ) = ∅ )
3	1 2	sylibr	⊢ ( 𝜑 → ( 𝐴 “ 𝐵 ) = ∅ )