MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax1 Structured version   Visualization version   GIF version

Theorem ax1 1582
Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Ref Expression
ax1 (𝜑 → (𝜓𝜑))

Proof of Theorem ax1
StepHypRef Expression
1 luklem5 1578 1 (𝜑 → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator