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Mirrors > Home > LLPE Home > Th. List > dismdac | Structured version |
Description: ⅋ distributes over &. |
Ref | Expression |
---|---|
dismdac.1 | ⊦ (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃))) |
Ref | Expression |
---|---|
dismdac | ⊦ (𝜑 ⅋ ((𝜓 ⅋ 𝜒) & (𝜓 ⅋ 𝜃))) |
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))) |
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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