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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 256 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | imp31 254 | 1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem is referenced by: sbc2iedv 2985 csbie2t 3053 foco2 5663 erth 6481 distrlem1prl 7414 distrlem1pru 7415 uz11 9372 elpq 9467 divgcdcoprm0 11818 cncongr1 11820 efltlemlt 12903 |
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