Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3anidm12p2 Unicode version

Theorem 3anidm12p2 28582
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
3anidm12p2.1  |-  ( ( ps  /\  ph  /\  ph )  ->  ch )
Assertion
Ref Expression
3anidm12p2  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem 3anidm12p2
StepHypRef Expression
1 3anrot 939 . . 3  |-  ( ( ps  /\  ph  /\  ph )  <->  ( ph  /\  ph 
/\  ps ) )
2 3anidm12p2.1 . . 3  |-  ( ( ps  /\  ph  /\  ph )  ->  ch )
31, 2sylbir 204 . 2  |-  ( (
ph  /\  ph  /\  ps )  ->  ch )
433anidm12 1239 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator