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Theorem bj-pr2eq 34851
Description: Substitution property for pr2. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-pr2eq (𝐴 = 𝐵 → pr2 𝐴 = pr2 𝐵)

Proof of Theorem bj-pr2eq
StepHypRef Expression
1 bj-projeq2 34828 . 2 (𝐴 = 𝐵 → (1o Proj 𝐴) = (1o Proj 𝐵))
2 df-bj-pr2 34850 . 2 pr2 𝐴 = (1o Proj 𝐴)
3 df-bj-pr2 34850 . 2 pr2 𝐵 = (1o Proj 𝐵)
41, 2, 33eqtr4g 2798 1 (𝐴 = 𝐵 → pr2 𝐴 = pr2 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  1oc1o 8126   Proj bj-cproj 34825  pr2 bj-cpr2 34849
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-rab 3062  df-v 3400  df-un 3848  df-in 3850  df-ss 3860  df-sn 4517  df-pr 4519  df-op 4523  df-br 5031  df-opab 5093  df-xp 5531  df-cnv 5533  df-dm 5535  df-rn 5536  df-res 5537  df-ima 5538  df-bj-proj 34826  df-bj-pr2 34850
This theorem is referenced by:  bj-pr22val  34854  bj-2uplth  34856
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