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Theorem s3eq2 14906
Description: Equality theorem for a length 3 word for the second symbol. (Contributed by AV, 4-Jan-2022.)
Assertion
Ref Expression
s3eq2 (𝐵 = 𝐷 → ⟨“𝐴𝐵𝐶”⟩ = ⟨“𝐴𝐷𝐶”⟩)

Proof of Theorem s3eq2
StepHypRef Expression
1 eqidd 2736 . 2 (𝐵 = 𝐷𝐴 = 𝐴)
2 id 22 . 2 (𝐵 = 𝐷𝐵 = 𝐷)
3 eqidd 2736 . 2 (𝐵 = 𝐷𝐶 = 𝐶)
41, 2, 3s3eqd 14900 1 (𝐵 = 𝐷 → ⟨“𝐴𝐵𝐶”⟩ = ⟨“𝐴𝐷𝐶”⟩)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  ⟨“cs3 14878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-s1 14631  df-s2 14884  df-s3 14885
This theorem is referenced by:  tgcgrxfr  28541  isperp2  28738  elwwlks2ons3  29985  frgr2wwlk1  30358  frgr2wwlkeqm  30360  fusgr2wsp2nb  30363
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