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Theorem seqeq2d 11322
Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.)
Hypothesis
Ref Expression
seqeqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
seqeq2d  |-  ( ph  ->  seq  M ( A ,  F )  =  seq  M ( B ,  F ) )

Proof of Theorem seqeq2d
StepHypRef Expression
1 seqeqd.1 . 2  |-  ( ph  ->  A  =  B )
2 seqeq2 11319 . 2  |-  ( A  =  B  ->  seq  M ( A ,  F
)  =  seq  M
( B ,  F
) )
31, 2syl 16 1  |-  ( ph  ->  seq  M ( A ,  F )  =  seq  M ( B ,  F ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    seq cseq 11315
This theorem is referenced by:  seqeq123d  11324  sadfval  12956  smufval  12981  gsumvalx  14766  gsumpropd  14768  gsumress  14769  mulgfval  14883  submmulg  14917  subgmulg  14950  dvnfval  19800
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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