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Theorem psseq1i 3996
 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
psseq1i (𝐴𝐶𝐵𝐶)

Proof of Theorem psseq1i
StepHypRef Expression
1 psseq1i.1 . 2 𝐴 = 𝐵
2 psseq1 3994 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶𝐵𝐶)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   = wceq 1539   ⊊ wpss 3860 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 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-ne 2953  df-v 3412  df-in 3866  df-ss 3876  df-pss 3878 This theorem is referenced by:  psseq12i  3998
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