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Theorem seqeq123d 10259
 Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.)
Hypotheses
Ref Expression
seqeq123d.1
seqeq123d.2
seqeq123d.3
Assertion
Ref Expression
seqeq123d

Proof of Theorem seqeq123d
StepHypRef Expression
1 seqeq123d.1 . . 3
21seqeq1d 10256 . 2
3 seqeq123d.2 . . 3
43seqeq2d 10257 . 2
5 seqeq123d.3 . . 3
65seqeq3d 10258 . 2
72, 4, 63eqtrd 2177 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332   cseq 10250 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3080  df-in 3082  df-ss 3089  df-sn 3538  df-pr 3539  df-op 3541  df-uni 3745  df-br 3938  df-opab 3998  df-mpt 3999  df-cnv 4555  df-dm 4557  df-rn 4558  df-res 4559  df-iota 5096  df-fv 5139  df-ov 5785  df-oprab 5786  df-mpo 5787  df-recs 6210  df-frec 6296  df-seqfrec 10251 This theorem is referenced by: (None)
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