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Theorem prm 3727
Description: A pair containing a set is inhabited. (Contributed by Jim Kingdon, 21-Sep-2018.)
Hypothesis
Ref Expression
prnz.1 𝐴 ∈ V
Assertion
Ref Expression
prm 𝑥 𝑥 ∈ {𝐴, 𝐵}
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵

Proof of Theorem prm
StepHypRef Expression
1 prnz.1 . 2 𝐴 ∈ V
2 prmg 3725 . 2 (𝐴 ∈ V → ∃𝑥 𝑥 ∈ {𝐴, 𝐵})
31, 2ax-mp 5 1 𝑥 𝑥 ∈ {𝐴, 𝐵}
Colors of variables: wff set class
Syntax hints:  wex 1502  wcel 2158  Vcvv 2749  {cpr 3605
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-sn 3610  df-pr 3611
This theorem is referenced by: (None)
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