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Theorem mdasd 13
Description: is associative. Deduction form of ax-mdas 9.
Hypothesis
Ref Expression
mdasd.1 (𝜃 ⅋ ((𝜑𝜓) ⅋ 𝜒))
Assertion
Ref Expression
mdasd (𝜃 ⅋ (𝜑 ⅋ (𝜓𝜒)))

Proof of Theorem mdasd
StepHypRef Expression
1 mdasd.1 . 2 (𝜃 ⅋ ((𝜑𝜓) ⅋ 𝜒))
2 ax-mdas 9 . 2 (~ ((𝜑𝜓) ⅋ 𝜒) ⅋ (𝜑 ⅋ (𝜓𝜒)))
31, 2ax-cut 6 1 (𝜃 ⅋ (𝜑 ⅋ (𝜓𝜒)))
Colors of variables: wff var nilad
Syntax hints:  wmd 2
This theorem was proved from axioms:  ax-cut 6  ax-mdas 9
This theorem is referenced by: (None)
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