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Theorem mpani 657
Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)
Hypotheses
Ref Expression
mpani.1
mpani.2
Assertion
Ref Expression
mpani

Proof of Theorem mpani
StepHypRef Expression
1 mpani.1 . . 3
21a1i 10 . 2
3 mpani.2 . 2
42, 3mpand 656 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358
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 177  df-an 360
This theorem is referenced by:  mp2ani  659
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