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Theorem uun0.1 31814
Description: Convention notation form of un0.1 31815. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
uun0.1.1  |-  ( T. 
->  ph )
uun0.1.2  |-  ( ps 
->  ch )
uun0.1.3  |-  ( ( T.  /\  ps )  ->  th )
Assertion
Ref Expression
uun0.1  |-  ( ps 
->  th )

Proof of Theorem uun0.1
StepHypRef Expression
1 tru 1374 . 2  |- T.
2 uun0.1.1 . . . . . 6  |-  ( T. 
->  ph )
3 uun0.1.2 . . . . . 6  |-  ( ps 
->  ch )
42, 3pm3.2i 455 . . . . 5  |-  ( ( T.  ->  ph )  /\  ( ps  ->  ch )
)
5 uun0.1.3 . . . . 5  |-  ( ( T.  /\  ps )  ->  th )
64, 5pm3.2i 455 . . . 4  |-  ( ( ( T.  ->  ph )  /\  ( ps  ->  ch ) )  /\  (
( T.  /\  ps )  ->  th ) )
76simpri 462 . . 3  |-  ( ( T.  /\  ps )  ->  th )
87ex 434 . 2  |-  ( T. 
->  ( ps  ->  th )
)
91, 8ax-mp 5 1  |-  ( ps 
->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   T. wtru 1371
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-tru 1373
This theorem is referenced by:  un0.1  31815  sspwimp  31957
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