Theorem pssned

Description: Proper subclasses are unequal. Deduction form of pssne . (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	pssssd.1	⊢ ( 𝜑 → 𝐴 ⊊ 𝐵 )
Assertion	pssned	⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		pssssd.1	⊢ ( 𝜑 → 𝐴 ⊊ 𝐵 )
2		pssne	⊢ ( 𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )