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Theorem sseqtrrdi 3146
Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtrrdi.1  |-  ( ph  ->  A  C_  B )
sseqtrrdi.2  |-  C  =  B
Assertion
Ref Expression
sseqtrrdi  |-  ( ph  ->  A  C_  C )

Proof of Theorem sseqtrrdi
StepHypRef Expression
1 sseqtrrdi.1 . 2  |-  ( ph  ->  A  C_  B )
2 sseqtrrdi.2 . . 3  |-  C  =  B
32eqcomi 2143 . 2  |-  B  =  C
41, 3sseqtrdi 3145 1  |-  ( ph  ->  A  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331    C_ wss 3071
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084
This theorem is referenced by:  iunpw  4401  iotanul  5103  iotass  5105  tfrlem9  6216  tfrlemibfn  6225  tfrlemiubacc  6227  tfrlemi14d  6230  tfr1onlemssrecs  6236  tfr1onlemres  6246  tfrcllemres  6259  exmidfodomrlemr  7058  exmidfodomrlemrALT  7059  uznnssnn  9379  shftfvalg  10597  shftfval  10600  clim2prod  11315  eltopss  12186  difopn  12287  tgrest  12348  txuni2  12435  tgioo  12725
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