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

Theorem pm1.4 863
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 862 . 2 (𝜑 → (𝜓𝜑))
2 orc 861 . 2 (𝜓 → (𝜓𝜑))
31, 2jaoi 851 1 ((𝜑𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 841
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 208  df-or 842
This theorem is referenced by:  orcom  864  orcoms  868  pm2.3  918  pm2.36  963  pm2.37  964  rb-ax2  1745  prneimg  4777  cnf2dd  35250  orcomdd  35326  rp-fakeanorass  39757  orbi1rVD  41059  itsclc0yqsol  44679
  Copyright terms: Public domain W3C validator