MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  orim1i Structured version   Visualization version   GIF version

Theorem orim1i 538
Description: Introduce disjunct to both sides of an implication. (Contributed by NM, 6-Jun-1994.)
Hypothesis
Ref Expression
orim1i.1 (𝜑𝜓)
Assertion
Ref Expression
orim1i ((𝜑𝜒) → (𝜓𝜒))

Proof of Theorem orim1i
StepHypRef Expression
1 orim1i.1 . 2 (𝜑𝜓)
2 id 22 . 2 (𝜒𝜒)
31, 2orim12i 537 1 ((𝜑𝜒) → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382
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 384
This theorem is referenced by:  nfntOLDOLD  1823  19.34  1958  r19.45v  3124  nnm1nn0  11372  elfzo0l  12598  xrge0iifhom  30111  bj-andnotim  32698  orfa2  34017  expdioph  37907  ifpimim  38171
  Copyright terms: Public domain W3C validator