Theorem ineqcomi

Description: Disjointness inference (when C = (/) ), inference form of ineqcom . (Contributed by Peter Mazsa, 26-Mar-2017)

	Ref	Expression
Hypothesis	ineqcomi.1	⊢ ( 𝐴 ∩ 𝐵 ) = 𝐶
Assertion	ineqcomi	⊢ ( 𝐵 ∩ 𝐴 ) = 𝐶

Proof

Step	Hyp	Ref	Expression
1		ineqcomi.1	⊢ ( 𝐴 ∩ 𝐵 ) = 𝐶
2		ineqcom	⊢ ( ( 𝐴 ∩ 𝐵 ) = 𝐶 ↔ ( 𝐵 ∩ 𝐴 ) = 𝐶 )
3	1 2	mpbi	⊢ ( 𝐵 ∩ 𝐴 ) = 𝐶