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Theorem seqeq2d 10255
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 10252 . 2  |-  ( A  =  B  ->  seq M ( A ,  F )  =  seq M ( B ,  F ) )
31, 2syl 14 1  |-  ( ph  ->  seq M ( A ,  F )  =  seq M ( B ,  F ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332    seqcseq 10248
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-opab 3997  df-mpt 3998  df-cnv 4554  df-dm 4556  df-rn 4557  df-res 4558  df-iota 5095  df-fv 5138  df-ov 5784  df-oprab 5785  df-mpo 5786  df-recs 6209  df-frec 6295  df-seqfrec 10249
This theorem is referenced by:  seqeq123d  10257
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