Theorem psseq2i 4091

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

Hypothesis

Ref	Expression
psseq1i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
psseq2i	⊢ (𝐶 ⊊ 𝐴 ↔ 𝐶 ⊊ 𝐵)

Proof of Theorem psseq2i

Step	Hyp	Ref	Expression
1		psseq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		psseq2 4089	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 ⊊ 𝐴 ↔ 𝐶 ⊊ 𝐵))
3	1, 2	ax-mp 5	1 ⊢ (𝐶 ⊊ 𝐴 ↔ 𝐶 ⊊ 𝐵)

Syntax hints:   ↔ wb 205   = wceq 1542   ⊊ wpss 3950

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2942  df-v 3477  df-in 3956  df-ss 3966  df-pss 3968

This theorem is referenced by:  psseq12i  4092  disjpss  4461  infeq5i  9631