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Theorem bj-pr2ex 35839
Description: Sethood of the second projection. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-pr2ex (𝐴𝑉 → pr2 𝐴 ∈ V)

Proof of Theorem bj-pr2ex
StepHypRef Expression
1 df-bj-pr2 35834 . 2 pr2 𝐴 = (1o Proj 𝐴)
2 bj-projex 35814 . 2 (𝐴𝑉 → (1o Proj 𝐴) ∈ V)
31, 2eqeltrid 2838 1 (𝐴𝑉 → pr2 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3475  1oc1o 8454   Proj bj-cproj 35809  pr2 bj-cpr2 35833
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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-rep 5284  ax-sep 5298  ax-nul 5305  ax-pr 5426  ax-un 7720
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-sbc 3777  df-csb 3893  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4322  df-if 4528  df-sn 4628  df-pr 4630  df-op 4634  df-uni 4908  df-br 5148  df-opab 5210  df-xp 5681  df-cnv 5683  df-dm 5685  df-rn 5686  df-res 5687  df-ima 5688  df-bj-proj 35810  df-bj-pr2 35834
This theorem is referenced by:  bj-2uplex  35841
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