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Theorem bj-pr1eq 34929
Description: Substitution property for pr1. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-pr1eq (𝐴 = 𝐵 → pr1 𝐴 = pr1 𝐵)

Proof of Theorem bj-pr1eq
StepHypRef Expression
1 bj-projeq2 34920 . 2 (𝐴 = 𝐵 → (∅ Proj 𝐴) = (∅ Proj 𝐵))
2 df-bj-pr1 34928 . 2 pr1 𝐴 = (∅ Proj 𝐴)
3 df-bj-pr1 34928 . 2 pr1 𝐵 = (∅ Proj 𝐵)
41, 2, 33eqtr4g 2803 1 (𝐴 = 𝐵 → pr1 𝐴 = pr1 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1543  c0 4237   Proj bj-cproj 34917  pr1 bj-cpr1 34927
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3070  df-v 3410  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-if 4440  df-sn 4542  df-pr 4544  df-op 4548  df-br 5054  df-opab 5116  df-xp 5557  df-cnv 5559  df-dm 5561  df-rn 5562  df-res 5563  df-ima 5564  df-bj-proj 34918  df-bj-pr1 34928
This theorem is referenced by:  bj-pr11val  34932  bj-1uplth  34934  bj-pr21val  34940  bj-2uplth  34948
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