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Theorem sseq12i 3052
Description: An equality inference for the subclass relationship. (Contributed by NM, 31-May-1999.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
sseq1i.1 𝐴 = 𝐵
sseq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
sseq12i (𝐴𝐶𝐵𝐷)

Proof of Theorem sseq12i
StepHypRef Expression
1 sseq1i.1 . 2 𝐴 = 𝐵
2 sseq12i.2 . 2 𝐶 = 𝐷
3 sseq12 3049 . 2 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))
41, 2, 3mp2an 417 1 (𝐴𝐶𝐵𝐷)
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1289  wss 2999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012
This theorem is referenced by:  3sstr3i  3064  3sstr4i  3065  3sstr3g  3066  3sstr4g  3067  ss2rab  3097
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