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Theorem sseqtrrdi 3205
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 3204 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wss 3130
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 3136  df-ss 3143
This theorem is referenced by:  iunpw  4481  iotanul  5194  iotass  5196  tfrlem9  6320  tfrlemibfn  6329  tfrlemiubacc  6331  tfrlemi14d  6334  tfr1onlemssrecs  6340  tfr1onlemres  6350  tfrcllemres  6363  exmidfodomrlemr  7201  exmidfodomrlemrALT  7202  uznnssnn  9577  shftfvalg  10827  shftfval  10830  clim2prod  11547  reldvdsrsrg  13261  dvdsrvald  13262  dvdsrex  13267  eltopss  13512  difopn  13611  tgrest  13672  txuni2  13759  tgioo  14049
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