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Theorem ltex 42286
Description: The less-than relation is a set. (Contributed by SN, 5-Jun-2025.)
Assertion
Ref Expression
ltex < ∈ V

Proof of Theorem ltex
StepHypRef Expression
1 xrex 13029 . . 3 * ∈ V
21, 1xpex 7773 . 2 (ℝ* × ℝ*) ∈ V
3 ltrelxr 11322 . 2 < ⊆ (ℝ* × ℝ*)
42, 3ssexi 5322 1 < ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  Vcvv 3480   × cxp 5683  *cxr 11294   < clt 11295
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pow 5365  ax-pr 5432  ax-un 7755  ax-cnex 11211  ax-resscn 11212
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-pw 4602  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-opab 5206  df-xp 5691  df-rel 5692  df-xr 11299  df-ltxr 11300
This theorem is referenced by: (None)
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