MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.4 Structured version   Unicode version

Theorem pm3.4 561
Description: Conjunction implies implication. Theorem *3.4 of [WhiteheadRussell] p. 113. (Contributed by NM, 31-Jul-1995.)
Assertion
Ref Expression
pm3.4  |-  ( (
ph  /\  ps )  ->  ( ph  ->  ps ) )

Proof of Theorem pm3.4
StepHypRef Expression
1 simpr 461 . 2  |-  ( (
ph  /\  ps )  ->  ps )
21a1d 25 1  |-  ( (
ph  /\  ps )  ->  ( ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  cases2  963  sbequ1  1935  afvres  30090
  Copyright terms: Public domain W3C validator