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Theorem bj-projeq2 35183
Description: Substitution property for Proj. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-projeq2 (𝐵 = 𝐶 → (𝐴 Proj 𝐵) = (𝐴 Proj 𝐶))

Proof of Theorem bj-projeq2
StepHypRef Expression
1 eqid 2738 . 2 𝐴 = 𝐴
2 bj-projeq 35182 . 2 (𝐴 = 𝐴 → (𝐵 = 𝐶 → (𝐴 Proj 𝐵) = (𝐴 Proj 𝐶)))
31, 2ax-mp 5 1 (𝐵 = 𝐶 → (𝐴 Proj 𝐵) = (𝐴 Proj 𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539   Proj bj-cproj 35180
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-br 5075  df-opab 5137  df-xp 5595  df-cnv 5597  df-dm 5599  df-rn 5600  df-res 5601  df-ima 5602  df-bj-proj 35181
This theorem is referenced by:  bj-pr1eq  35192  bj-pr2eq  35206
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