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Theorem extmdac 47
Description: extracts out of &. Converse of dismdac 46.
Hypothesis
Ref Expression
extmdac.1 (𝜑 ⅋ ((𝜓𝜒) & (𝜓𝜃)))
Assertion
Ref Expression
extmdac (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃)))

Proof of Theorem extmdac
StepHypRef Expression
1 extmdac.1 . . . . 5 (𝜑 ⅋ ((𝜓𝜒) & (𝜓𝜃)))
21eac1d 37 . . . 4 (𝜑 ⅋ (𝜓𝜒))
32mdasri 17 . . 3 ((𝜑𝜓) ⅋ 𝜒)
41eac2d 39 . . . 4 (𝜑 ⅋ (𝜓𝜃))
54mdasri 17 . . 3 ((𝜑𝜓) ⅋ 𝜃)
63, 5iac 35 . 2 ((𝜑𝜓) ⅋ (𝜒 & 𝜃))
76mdasi 14 1 (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃)))
Colors of variables: wff var nilad
Syntax hints:  wmd 2   & wac 30
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-iac 32  ax-eac1 33  ax-eac2 34
This theorem is referenced by: (None)
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