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Theorem sseqtrrdi 3204
Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtrrdi.1 (𝜑𝐴𝐵)
sseqtrrdi.2 𝐶 = 𝐵
Assertion
Ref Expression
sseqtrrdi (𝜑𝐴𝐶)

Proof of Theorem sseqtrrdi
StepHypRef Expression
1 sseqtrrdi.1 . 2 (𝜑𝐴𝐵)
2 sseqtrrdi.2 . . 3 𝐶 = 𝐵
32eqcomi 2181 . 2 𝐵 = 𝐶
41, 3sseqtrdi 3203 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  iunpw  4480  iotanul  5193  iotass  5195  tfrlem9  6319  tfrlemibfn  6328  tfrlemiubacc  6330  tfrlemi14d  6333  tfr1onlemssrecs  6339  tfr1onlemres  6349  tfrcllemres  6362  exmidfodomrlemr  7200  exmidfodomrlemrALT  7201  uznnssnn  9576  shftfvalg  10826  shftfval  10829  clim2prod  11546  reldvdsrsrg  13259  dvdsrvald  13260  dvdsrex  13265  eltopss  13479  difopn  13578  tgrest  13639  txuni2  13726  tgioo  14016
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