Users' Mathboxes Mathbox for Giovanni Mascellani < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  tsim2 Structured version   Visualization version   GIF version

Theorem tsim2 32932
Description: A Tseitin axiom for logical implication, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsim2 (𝜃 → (𝜑 ∨ (𝜑𝜓)))

Proof of Theorem tsim2
StepHypRef Expression
1 pm2.21 118 . . 3 𝜑 → (𝜑𝜓))
21orri 389 . 2 (𝜑 ∨ (𝜑𝜓))
32a1i 11 1 (𝜃 → (𝜑 ∨ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-or 383
This theorem is referenced by:  mpt2bi123f  32965  ac6s6  32974
  Copyright terms: Public domain W3C validator