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Theorem seqeq2d 13109
 Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.)
Hypothesis
Ref Expression
seqeqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
seqeq2d (𝜑 → seq𝑀(𝐴, 𝐹) = seq𝑀(𝐵, 𝐹))

Proof of Theorem seqeq2d
StepHypRef Expression
1 seqeqd.1 . 2 (𝜑𝐴 = 𝐵)
2 seqeq2 13106 . 2 (𝐴 = 𝐵 → seq𝑀(𝐴, 𝐹) = seq𝑀(𝐵, 𝐹))
31, 2syl 17 1 (𝜑 → seq𝑀(𝐴, 𝐹) = seq𝑀(𝐵, 𝐹))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1656  seqcseq 13102 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-3an 1113  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rex 3123  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4147  df-if 4309  df-sn 4400  df-pr 4402  df-op 4406  df-uni 4661  df-br 4876  df-opab 4938  df-mpt 4955  df-xp 5352  df-cnv 5354  df-dm 5356  df-rn 5357  df-res 5358  df-ima 5359  df-pred 5924  df-iota 6090  df-fv 6135  df-ov 6913  df-oprab 6914  df-mpt2 6915  df-wrecs 7677  df-recs 7739  df-rdg 7777  df-seq 13103 This theorem is referenced by:  seqeq123d  13111  sadfval  15554  smufval  15579  gsumvalx  17630  gsumpropd  17632  gsumress  17636  mulgfval  17903  submmulg  17944  subgmulg  17966  dvnfval  24091
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