Users' Mathboxes Mathbox for Peter Mazsa < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  el3v1 Structured version   Visualization version   GIF version

Theorem el3v1 37692
Description: New way (elv 3477, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)
Hypothesis
Ref Expression
el3v1.1 ((𝑥 ∈ V ∧ 𝜓𝜒) → 𝜃)
Assertion
Ref Expression
el3v1 ((𝜓𝜒) → 𝜃)

Proof of Theorem el3v1
StepHypRef Expression
1 vex 3475 . 2 𝑥 ∈ V
2 el3v1.1 . 2 ((𝑥 ∈ V ∧ 𝜓𝜒) → 𝜃)
31, 2mp3an1 1445 1 ((𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1085  wcel 2099  Vcvv 3471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473
This theorem is referenced by:  el3v12  37695  br1cossxrnres  37920
  Copyright terms: Public domain W3C validator