Theorem psstrd

Description: Proper subclass inclusion is transitive. Deduction form of psstr . (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypotheses	psstrd.1	⊢ ( 𝜑 → 𝐴 ⊊ 𝐵 )
	psstrd.2	⊢ ( 𝜑 → 𝐵 ⊊ 𝐶 )
Assertion	psstrd	⊢ ( 𝜑 → 𝐴 ⊊ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		psstrd.1	⊢ ( 𝜑 → 𝐴 ⊊ 𝐵 )
2		psstrd.2	⊢ ( 𝜑 → 𝐵 ⊊ 𝐶 )
3		psstr	⊢ ( ( 𝐴 ⊊ 𝐵 ∧ 𝐵 ⊊ 𝐶 ) → 𝐴 ⊊ 𝐶 )
4	1 2 3	syl2anc	⊢ ( 𝜑 → 𝐴 ⊊ 𝐶 )