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Theorem mp2ani 416
Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mp2ani.1 𝜓
mp2ani.2 𝜒
mp2ani.3 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
mp2ani (𝜑𝜃)

Proof of Theorem mp2ani
StepHypRef Expression
1 mp2ani.2 . 2 𝜒
2 mp2ani.1 . . 3 𝜓
3 mp2ani.3 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
42, 3mpani 414 . 2 (𝜑 → (𝜒𝜃))
51, 4mpi 15 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  th3q  6242  addnnnq0  6605  mulnnnq0  6606  addsrpr  6888  mulsrpr  6889
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