MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm1.4 Structured version   Visualization version   GIF version

Theorem pm1.4 849
Description: Axiom *1.4 of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm1.4 ((𝜑𝜓) → (𝜓𝜑))

Proof of Theorem pm1.4
StepHypRef Expression
1 olc 848 . 2 (𝜑 → (𝜓𝜑))
2 orc 847 . 2 (𝜓 → (𝜓𝜑))
31, 2jaoi 837 1 ((𝜑𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 826
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 197  df-or 827
This theorem is referenced by:  orcom  850  orcoms  852  pm2.3  889  pm2.36  950  pm2.37  951  rb-ax2  1825  nfntOLDOLD  1933  prneimg  4517  orcomdd  34216  rp-fakeanorass  38377  orbi1rVD  39599
  Copyright terms: Public domain W3C validator