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

Theorem ancr 547
Description: Conjoin antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.)
Assertion
Ref Expression
ancr ((𝜑𝜓) → (𝜑 → (𝜓𝜑)))

Proof of Theorem ancr
StepHypRef Expression
1 pm3.21 472 . 2 (𝜑 → (𝜓 → (𝜓𝜑)))
21a2i 14 1 ((𝜑𝜓) → (𝜑 → (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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-an 397
This theorem is referenced by:  bimsc1  838  reupick2  4288  intmin4  4898  bnj1098  31955  lukshef-ax2  33661  bj-opelid  34341  poimirlem25  34799  pm14.122b  40635
  Copyright terms: Public domain W3C validator