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

Theorem orcoms 871
Description: Commutation of disjuncts in antecedent. (Contributed by NM, 2-Dec-2012.)
Hypothesis
Ref Expression
orcoms.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
orcoms ((𝜓𝜑) → 𝜒)

Proof of Theorem orcoms
StepHypRef Expression
1 pm1.4 868 . 2 ((𝜓𝜑) → (𝜑𝜓))
2 orcoms.1 . 2 ((𝜑𝜓) → 𝜒)
31, 2syl 17 1 ((𝜓𝜑) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 846
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 210  df-or 847
This theorem is referenced by:  olcs  875  19.40b  1895  r19.30  3244  propeqop  5364  pwssun  5425  sorpsscmpl  7478  hashinfxadd  13838  swrdnd  14105  pfxnd0  14139  dvasin  35484  dvacos  35485  line2ylem  45631  line2xlem  45633
  Copyright terms: Public domain W3C validator