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Mirrors > Home > ILE Home > Th. List > imdistanri | GIF version |
Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.) |
Ref | Expression |
---|---|
imdistanri.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
imdistanri | ⊢ ((𝜓 ∧ 𝜑) → (𝜒 ∧ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imdistanri.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | com12 30 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
3 | 2 | impac 373 | 1 ⊢ ((𝜓 ∧ 𝜑) → (𝜒 ∧ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem is referenced by: (None) |
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