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Theorem 3impcombi 41516
Description: A 1-hypothesis propositional calculus deduction. (Contributed by Alan Sare, 25-Sep-2017.)
Hypothesis
Ref Expression
3impcombi.1 ((𝜑𝜓𝜑) → (𝜒𝜃))
Assertion
Ref Expression
3impcombi ((𝜓𝜑𝜒) → 𝜃)

Proof of Theorem 3impcombi
StepHypRef Expression
1 3impcombi.1 . . . . 5 ((𝜑𝜓𝜑) → (𝜒𝜃))
21biimpd 232 . . . 4 ((𝜑𝜓𝜑) → (𝜒𝜃))
323anidm13 1417 . . 3 ((𝜑𝜓) → (𝜒𝜃))
43ancoms 462 . 2 ((𝜓𝜑) → (𝜒𝜃))
543impia 1114 1 ((𝜓𝜑𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  isosctrlem1ALT  41633
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