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Theorem seqeq1d 10192
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
seqeq1d  |-  ( ph  ->  seq A (  .+  ,  F )  =  seq B (  .+  ,  F ) )

Proof of Theorem seqeq1d
StepHypRef Expression
1 seqeqd.1 . 2  |-  ( ph  ->  A  =  B )
2 seqeq1 10189 . 2  |-  ( A  =  B  ->  seq A (  .+  ,  F )  =  seq B (  .+  ,  F ) )
31, 2syl 14 1  |-  ( ph  ->  seq A (  .+  ,  F )  =  seq B (  .+  ,  F ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316    seqcseq 10186
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-opab 3960  df-mpt 3961  df-cnv 4517  df-dm 4519  df-rn 4520  df-res 4521  df-iota 5058  df-fv 5101  df-oprab 5746  df-mpo 5747  df-recs 6170  df-frec 6256  df-seqfrec 10187
This theorem is referenced by:  seqeq123d  10195  seq3f1olemqsum  10241  bcval5  10477  bcn2  10478  seq3shft  10578  iserex  11076  iser3shft  11083  isumsplit  11228  eftlub  11323
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