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Theorem bi123impia 36747
Description: 3impia 1203 with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi123impia.1  |-  ( (
ph  /\  ps )  <->  ( ch  <->  th ) )
Assertion
Ref Expression
bi123impia  |-  ( (
ph  /\  ps  /\  ch )  ->  th )

Proof of Theorem bi123impia
StepHypRef Expression
1 bi123impia.1 . . 3  |-  ( (
ph  /\  ps )  <->  ( ch  <->  th ) )
21biimpi 198 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
32biimp3a 1365 1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188    /\ wa 371    /\ w3a 983
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 985
This theorem is referenced by: (None)
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