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Theorem imim3i 59
Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.)
Hypothesis
Ref Expression
imim3i.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
imim3i ((𝜃𝜑) → ((𝜃𝜓) → (𝜃𝜒)))

Proof of Theorem imim3i
StepHypRef Expression
1 imim3i.1 . . 3 (𝜑 → (𝜓𝜒))
21imim2i 12 . 2 ((𝜃𝜑) → (𝜃 → (𝜓𝜒)))
32a2d 26 1 ((𝜃𝜑) → ((𝜃𝜓) → (𝜃𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  pm2.83  75  pm5.74  172  bi3ant  217  pm3.43i  262  ceqsalt  2597
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