Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-imn3ani Structured version   Visualization version   Unicode version

Theorem bj-imn3ani 31183
Description: Duplication of bnj1224 29625. Three-fold version of imnani 425. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by BJ, 22-Oct-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-imn3ani.1  |-  -.  ( ph  /\  ps  /\  ch )
Assertion
Ref Expression
bj-imn3ani  |-  ( (
ph  /\  ps )  ->  -.  ch )

Proof of Theorem bj-imn3ani
StepHypRef Expression
1 bj-imn3ani.1 . . 3  |-  -.  ( ph  /\  ps  /\  ch )
2 df-3an 988 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
31, 2mtbi 300 . 2  |-  -.  (
( ph  /\  ps )  /\  ch )
43imnani 425 1  |-  ( (
ph  /\  ps )  ->  -.  ch )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 371    /\ w3a 986
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 189  df-an 373  df-3an 988
This theorem is referenced by:  bj-inftyexpidisj  31664
  Copyright terms: Public domain W3C validator