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Theorem 3impcombi 28929
Description: A 1-hypothesis propositional calculus deduction (Contributed by Alan Sare, 25-Sep-2017.)
Hypothesis
Ref Expression
3impcombi.1  |-  ( (
ph  /\  ps  /\  ph )  ->  ( ch  <->  th )
)
Assertion
Ref Expression
3impcombi  |-  ( ( ps  /\  ph  /\  ch )  ->  th )

Proof of Theorem 3impcombi
StepHypRef Expression
1 3impcombi.1 . . . . 5  |-  ( (
ph  /\  ps  /\  ph )  ->  ( ch  <->  th )
)
21biimpd 199 . . . 4  |-  ( (
ph  /\  ps  /\  ph )  ->  ( ch  ->  th ) )
323anidm13 1242 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
43ancoms 440 . 2  |-  ( ( ps  /\  ph )  ->  ( ch  ->  th )
)
543impia 1150 1  |-  ( ( ps  /\  ph  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ w3a 936
This theorem is referenced by:  isosctrlem1ALT  29046
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator