Users' Mathboxes Mathbox for Peter Mazsa < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  el3v3 Structured version   Visualization version   GIF version

Theorem el3v3 35654
Description: New way (elv 3446, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.)
Hypothesis
Ref Expression
el3v3.1 ((𝜑𝜓𝑧 ∈ V) → 𝜃)
Assertion
Ref Expression
el3v3 ((𝜑𝜓) → 𝜃)

Proof of Theorem el3v3
StepHypRef Expression
1 vex 3444 . 2 𝑧 ∈ V
2 el3v3.1 . 2 ((𝜑𝜓𝑧 ∈ V) → 𝜃)
31, 2mp3an3 1447 1 ((𝜑𝜓) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084  wcel 2111  Vcvv 3441
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443
This theorem is referenced by:  el3v13  35656  el3v23  35657
  Copyright terms: Public domain W3C validator