Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  int3 Structured version   Unicode version

Theorem int3 33584
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 33584 is 3expia 1198. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
int3.1  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
Assertion
Ref Expression
int3  |-  (. (. ph ,. ps ).  ->.  ( ch  ->  th ) ).

Proof of Theorem int3
StepHypRef Expression
1 int3.1 . . . 4  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
21dfvd3ani 33558 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
323expia 1198 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
43dfvd2anir 33547 1  |-  (. (. ph ,. ps ).  ->.  ( ch  ->  th ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 33532   (.wvhc2 33543   (.wvhc3 33551
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  df-3an 975  df-vd1 33533  df-vhc2 33544  df-vhc3 33552
This theorem is referenced by:  suctrALTcfVD  33909
  Copyright terms: Public domain W3C validator