Theorem seqeq2d 10377

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

Step	Hyp	Ref	Expression
1		seqeqd.1	. 2 |- ( ph -> A = B )
2		seqeq2 10374	. 2 |- ( A = B -> seq M ( A , F ) = seq M ( B , F ) )
3	1, 2	syl 14	1 |- ( ph -> seq M ( A , F ) = seq M ( B , F ) )

Syntax hints:   -> wi 4   = wceq 1342   seqcseq 10370

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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-3an 969  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-ral 2447  df-rex 2448  df-v 2723  df-un 3115  df-in 3117  df-ss 3124  df-sn 3576  df-pr 3577  df-op 3579  df-uni 3784  df-br 3977  df-opab 4038  df-mpt 4039  df-cnv 4606  df-dm 4608  df-rn 4609  df-res 4610  df-iota 5147  df-fv 5190  df-ov 5839  df-oprab 5840  df-mpo 5841  df-recs 6264  df-frec 6350  df-seqfrec 10371

This theorem is referenced by:  seqeq123d  10379