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Theorem bj-pr1ex 36343
Description: Sethood of the first projection. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-pr1ex (𝐴𝑉 → pr1 𝐴 ∈ V)

Proof of Theorem bj-pr1ex
StepHypRef Expression
1 df-bj-pr1 36338 . 2 pr1 𝐴 = (∅ Proj 𝐴)
2 bj-projex 36332 . 2 (𝐴𝑉 → (∅ Proj 𝐴) ∈ V)
31, 2eqeltrid 2829 1 (𝐴𝑉 → pr1 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Vcvv 3466  c0 4314   Proj bj-cproj 36327  pr1 bj-cpr1 36337
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695  ax-rep 5275  ax-sep 5289  ax-nul 5296  ax-pr 5417  ax-un 7718
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2526  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-sbc 3770  df-csb 3886  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-uni 4900  df-br 5139  df-opab 5201  df-xp 5672  df-cnv 5674  df-dm 5676  df-rn 5677  df-res 5678  df-ima 5679  df-bj-proj 36328  df-bj-pr1 36338
This theorem is referenced by:  bj-1uplex  36345  bj-2uplex  36359
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