Theorem seqeq2d 12114

Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.)

Hypothesis

Ref	Expression
seqeqd.1

Assertion

Ref	Expression
seqeq2d

Proof of Theorem seqeq2d

Step	Hyp	Ref	Expression
1		seqeqd.1	. 2
2		seqeq2 12111	. 2
3	1, 2	syl 16	1

Syntax hints:  ->wi 4  =wceq 1395  seqcseq 12107

This theorem is referenced by:  seqeq123d  12116  sadfval  14102  smufval  14127  gsumvalx  15897  gsumpropd  15899  gsumress  15903  mulgfval  16143  submmulg  16177  subgmulg  16215  dvnfval  22325

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-recs 7061  df-rdg 7095  df-seq 12108