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Theorem s3eq2 14683
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 2737 . 2 (𝐵 = 𝐷𝐴 = 𝐴)
2 id 22 . 2 (𝐵 = 𝐷𝐵 = 𝐷)
3 eqidd 2737 . 2 (𝐵 = 𝐷𝐶 = 𝐶)
41, 2, 3s3eqd 14677 1 (𝐵 = 𝐷 → ⟨“𝐴𝐵𝐶”⟩ = ⟨“𝐴𝐷𝐶”⟩)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  ⟨“cs3 14655
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3404  df-v 3443  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4271  df-if 4475  df-sn 4575  df-pr 4577  df-op 4581  df-uni 4854  df-br 5094  df-iota 6432  df-fv 6488  df-ov 7341  df-s1 14401  df-s2 14661  df-s3 14662
This theorem is referenced by:  tgcgrxfr  27169  isperp2  27366  elwwlks2ons3  28609  frgr2wwlk1  28982  frgr2wwlkeqm  28984  fusgr2wsp2nb  28987
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