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Theorem mp4an 654
Description: An inference based on modus ponens. (Contributed by Jeff Madsen, 15-Jun-2010.)
Hypotheses
Ref Expression
mp4an.1
mp4an.2
mp4an.3
mp4an.4
mp4an.5
Assertion
Ref Expression
mp4an

Proof of Theorem mp4an
StepHypRef Expression
1 mp4an.1 . . 3
2 mp4an.2 . . 3
31, 2pm3.2i 441 . 2
4 mp4an.3 . . 3
5 mp4an.4 . . 3
64, 5pm3.2i 441 . 2
7 mp4an.5 . 2
83, 6, 7mp2an 653 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  tfin0c  4497  tc0c  6163  tcdi  6164  tc1c  6165
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