MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mptrabexOLD Structured version   Visualization version   GIF version

Theorem mptrabexOLD 6371
Description: Obsolete version of mptrabex 6370 as of 26-Mar-2021. (Contributed by AV, 16-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
mptrabexOLD.1 𝐴𝑉
Assertion
Ref Expression
mptrabexOLD (𝑥 ∈ {𝑦𝐴𝜑} ↦ 𝐵) ∈ V
Distinct variable groups:   𝑥,𝑦,𝐴   𝜑,𝑥
Allowed substitution hints:   𝜑(𝑦)   𝐵(𝑥,𝑦)   𝑉(𝑥,𝑦)

Proof of Theorem mptrabexOLD
StepHypRef Expression
1 mptrabexOLD.1 . . . 4 𝐴𝑉
21elexi 3185 . . 3 𝐴 ∈ V
32rabex 4735 . 2 {𝑦𝐴𝜑} ∈ V
43mptex 6368 1 (𝑥 ∈ {𝑦𝐴𝜑} ↦ 𝐵) ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 1976  {crab 2899  Vcvv 3172  cmpt 4637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-rep 4693  ax-sep 4703  ax-nul 4712  ax-pr 4828
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ne 2781  df-ral 2900  df-rex 2901  df-reu 2902  df-rab 2904  df-v 3174  df-sbc 3402  df-csb 3499  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-iun 4451  df-br 4578  df-opab 4638  df-mpt 4639  df-id 4943  df-xp 5034  df-rel 5035  df-cnv 5036  df-co 5037  df-dm 5038  df-rn 5039  df-res 5040  df-ima 5041  df-iota 5754  df-fun 5792  df-fn 5793  df-f 5794  df-f1 5795  df-fo 5796  df-f1o 5797  df-fv 5798
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator