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Theorem eqimssi 3027
Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1 𝐴 = 𝐵
Assertion
Ref Expression
eqimssi 𝐴𝐵

Proof of Theorem eqimssi
StepHypRef Expression
1 ssid 2992 . 2 𝐴𝐴
2 eqimssi.1 . 2 𝐴 = 𝐵
31, 2sseqtri 3005 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1259  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  funi  4960  fpr  5373  elfzo1  9148
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