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Theorem nic-stdmp 1465
Description: Derive the standard modus ponens from nic-mp 1446. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-smin  |-  ph
nic-smaj  |-  ( ph  ->  ps )
Assertion
Ref Expression
nic-stdmp  |-  ps

Proof of Theorem nic-stdmp
StepHypRef Expression
1 nic-smin . 2  |-  ph
2 nic-smaj . . 3  |-  ( ph  ->  ps )
3 nic-dfim 1444 . . . 4  |-  ( ( ( ph  -/\  ( ps  -/\  ps ) ) 
-/\  ( ph  ->  ps ) )  -/\  (
( ( ph  -/\  ( ps  -/\  ps ) ) 
-/\  ( ph  -/\  ( ps  -/\  ps ) ) )  -/\  ( ( ph  ->  ps )  -/\  ( ph  ->  ps )
) ) )
43nic-bi2 1464 . . 3  |-  ( (
ph  ->  ps )  -/\  ( ( ph  -/\  ( ps  -/\  ps ) ) 
-/\  ( ph  -/\  ( ps  -/\  ps ) ) ) )
52, 4nic-mp 1446 . 2  |-  ( ph  -/\  ( ps  -/\  ps )
)
61, 5nic-mp 1446 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    -/\ wnan 1297
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 179  df-or 361  df-an 362  df-nan 1298
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