Theorem psseq12i

Description: An equality inference for the proper subclass relationship. (Contributed by NM, 9-Jun-2004)

	Ref	Expression
Hypotheses	psseq1i.1	⊢ 𝐴 = 𝐵
	psseq12i.2	⊢ 𝐶 = 𝐷
Assertion	psseq12i	⊢ ( 𝐴 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐷 )

Proof

Step	Hyp	Ref	Expression
1		psseq1i.1	⊢ 𝐴 = 𝐵
2		psseq12i.2	⊢ 𝐶 = 𝐷
3	1	psseq1i	⊢ ( 𝐴 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐶 )
4	2	psseq2i	⊢ ( 𝐵 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐷 )
5	3 4	bitri	⊢ ( 𝐴 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐷 )