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Mirrors > Home > ILE Home > Th. List > impl | GIF version |
Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
impl.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Ref | Expression |
---|---|
impl | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | impl.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) | |
2 | 1 | expd 245 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | imp31 243 | 1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem is referenced by: sbc2iedv 2830 csbie2t 2894 foco2 5318 erth 6150 distrlem1prl 6680 distrlem1pru 6681 uz11 8495 |
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