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Theorem s3eq2 14756
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 14750 1 (𝐵 = 𝐷 → ⟨“𝐴𝐵𝐶”⟩ = ⟨“𝐴𝐷𝐶”⟩)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541  ⟨“cs3 14728
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3407  df-v 3446  df-dif 3912  df-un 3914  df-in 3916  df-ss 3926  df-nul 4282  df-if 4486  df-sn 4586  df-pr 4588  df-op 4592  df-uni 4865  df-br 5105  df-iota 6446  df-fv 6502  df-ov 7357  df-s1 14481  df-s2 14734  df-s3 14735
This theorem is referenced by:  tgcgrxfr  27358  isperp2  27555  elwwlks2ons3  28798  frgr2wwlk1  29171  frgr2wwlkeqm  29173  fusgr2wsp2nb  29176
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