Theorem psseq1i

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

	Ref	Expression
Hypothesis	psseq1i.1	⊢ 𝐴 = 𝐵
Assertion	psseq1i	⊢ ( 𝐴 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		psseq1i.1	⊢ 𝐴 = 𝐵
2		psseq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ⊊ 𝐶 ↔ 𝐵 ⊊ 𝐶 )