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Theorem nic-stdmp 1615
Description: Derive the standard modus ponens from nic-mp 1596. (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 1594 . . . 4 |- ( ( ( ph -/\ ( ps -/\ ps ) ) -/\ ( ph -> ps ) ) -/\ ( ( ( ph -/\ ( ps -/\ ps ) ) -/\ ( ph -/\ ( ps -/\ ps ) ) ) -/\ ( ( ph -> ps ) -/\ ( ph -> ps ) ) ) )
43nic-bi2 1614 . . 3 |- ( ( ph -> ps ) -/\ ( ( ph -/\ ( ps -/\ ps ) ) -/\ ( ph -/\ ( ps -/\ ps ) ) ) )
52, 4nic-mp 1596 . 2 |- ( ph -/\ ( ps -/\ ps ) )
61, 5nic-mp 1596 1 |- ps
Colors of variables: wff setvar class
Syntax hints:   -> wi 4   -/\ wnan 1447
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 197  df-or 385  df-an 386  df-nan 1448
This theorem is referenced by: (None)
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