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Theorem prm 3678
 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 3676 . 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 1469   ∈ wcel 2125  Vcvv 2709  {cpr 3557 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563 This theorem is referenced by: (None)
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