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Theorem seqeq2d 11250
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 11247 . 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 1649    seq cseq 11243
This theorem is referenced by:  seqeq123d  11252  sadfval  12884  smufval  12909  gsumvalx  14694  gsumpropd  14696  gsumress  14697  mulgfval  14811  submmulg  14845  subgmulg  14878  dvnfval  19668
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-uni 3951  df-br 4147  df-opab 4201  df-mpt 4202  df-cnv 4819  df-dm 4821  df-rn 4822  df-res 4823  df-ima 4824  df-iota 5351  df-fv 5395  df-ov 6016  df-oprab 6017  df-mpt2 6018  df-recs 6562  df-rdg 6597  df-seq 11244
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