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Theorem biijust 580
Description: Theorem used to justify definition of intuitionistic biconditional df-bi 114. (Contributed by NM, 24-Nov-2017.)
Assertion
Ref Expression
biijust  |-  ( ( ( ( ph  ->  ps )  /\  ( ps 
->  ph ) )  -> 
( ( ph  ->  ps )  /\  ( ps 
->  ph ) ) )  /\  ( ( (
ph  ->  ps )  /\  ( ps  ->  ph )
)  ->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) ) )

Proof of Theorem biijust
StepHypRef Expression
1 id 19 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  ->  (
( ph  ->  ps )  /\  ( ps  ->  ph )
) )
21, 1pm3.2i 261 1  |-  ( ( ( ( ph  ->  ps )  /\  ( ps 
->  ph ) )  -> 
( ( ph  ->  ps )  /\  ( ps 
->  ph ) ) )  /\  ( ( (
ph  ->  ps )  /\  ( ps  ->  ph )
)  ->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105
This theorem is referenced by: (None)
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