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Theorem seqeq123d 11324
 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 11321 . 2
3 seqeq123d.2 . . 3
43seqeq2d 11322 . 2
5 seqeq123d.3 . . 3
65seqeq3d 11323 . 2
72, 4, 63eqtrd 2471 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   cseq 11315 This theorem is referenced by:  relexp0  25121  relexpsucr  25122 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fv 5454  df-ov 6076  df-oprab 6077  df-mpt2 6078  df-recs 6625  df-rdg 6660  df-seq 11316
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