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Mirrors > Home > ILE Home > Th. List > expl | GIF version |
Description: Export a wff from a left conjunct. (Contributed by Jeff Hankins, 28-Aug-2009.) |
Ref | Expression |
---|---|
expl.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
expl | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | expl.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
2 | 1 | exp31 364 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | impd 254 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem is referenced by: ssenen 6845 recclnq 7382 shftfvalg 10811 shftfval 10814 fsum2dlemstep 11426 fprod2dlemstep 11614 prmpwdvds 12336 tgtop 13235 |
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