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Theorem stoic1b 1695
Description: Stoic logic Thema 1 (part b). The other part of thema 1 of Stoic logic; see stoic1a 1694. (Contributed by David A. Wheeler, 16-Feb-2019.)
Hypothesis
Ref Expression
stoic1.1 ((𝜑𝜓) → 𝜃)
Assertion
Ref Expression
stoic1b ((𝜓 ∧ ¬ 𝜃) → ¬ 𝜑)

Proof of Theorem stoic1b
StepHypRef Expression
1 stoic1.1 . . 3 ((𝜑𝜓) → 𝜃)
21ancoms 469 . 2 ((𝜓𝜑) → 𝜃)
32stoic1a 1694 1 ((𝜓 ∧ ¬ 𝜃) → ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 384
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 386
This theorem is referenced by:  hashdomi  13109  hfext  31929
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