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Theorem imp45 416
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
imp45 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) → 𝜏)

Proof of Theorem imp45
StepHypRef Expression
1 imp4.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21imp4d 411 . 2 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
32imp 393 1 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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-an 383
This theorem is referenced by:  alexsubALTlem3  22073  spansncvi  28851  atcvatlem  29584
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