Theorem dismdac 46

Description: ⅋ distributes over &.

Hypothesis

Ref	Expression
dismdac.1	⊦ (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃)))

Assertion

Ref	Expression
dismdac	⊦ (𝜑 ⅋ ((𝜓 ⅋ 𝜒) & (𝜓 ⅋ 𝜃)))

Proof of Theorem dismdac

Step	Hyp	Ref	Expression
1		dismdac.1	. . . . 5 ⊦ (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃)))
2	1	mdasri 17	. . . 4 ⊦ ((𝜑 ⅋ 𝜓) ⅋ (𝜒 & 𝜃))
3	2	eac1d 37	. . 3 ⊦ ((𝜑 ⅋ 𝜓) ⅋ 𝜒)
4	3	mdasi 14	. 2 ⊦ (𝜑 ⅋ (𝜓 ⅋ 𝜒))
5	2	eac2d 39	. . 3 ⊦ ((𝜑 ⅋ 𝜓) ⅋ 𝜃)
6	5	mdasi 14	. 2 ⊦ (𝜑 ⅋ (𝜓 ⅋ 𝜃))
7	4, 6	iac 35	1 ⊦ (𝜑 ⅋ ((𝜓 ⅋ 𝜒) & (𝜓 ⅋ 𝜃)))

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)