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Theorem mp2d 47
Description: A double modus ponens deduction. (Contributed by NM, 23-May-2013.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)
Hypotheses
Ref Expression
mp2d.1 (𝜑𝜓)
mp2d.2 (𝜑𝜒)
mp2d.3 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
mp2d (𝜑𝜃)

Proof of Theorem mp2d
StepHypRef Expression
1 mp2d.1 . 2 (𝜑𝜓)
2 mp2d.2 . . 3 (𝜑𝜒)
3 mp2d.3 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
42, 3mpid 42 . 2 (𝜑 → (𝜓𝜃))
51, 4mpd 13 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  fisseneq  6906  prloc  7442  axcaucvglemres  7850  bezoutlemmain  11942  coprm  12087  sqrt2irr  12105  oddprmdvds  12295  xblss2ps  13159  xblss2  13160  lgsprme0  13698  pw1nct  13998  apdiff  14042
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