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Theorem psseq1i 3033
 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 3031 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶𝐵𝐶)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1243   ⊊ wpss 2918 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ne 2206  df-in 2924  df-ss 2931  df-pss 2933 This theorem is referenced by:  psseq12i  3035
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