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Mirrors > Home > ILE Home > Th. List > exp4b | GIF version |
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Nov-2012.) |
Ref | Expression |
---|---|
exp4b.1 | ⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → 𝜏)) |
Ref | Expression |
---|---|
exp4b | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp4b.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → 𝜏)) | |
2 | 1 | ex 114 | . 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
3 | 2 | exp4a 363 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
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 depends on definitions: df-bi 116 |
This theorem is referenced by: exp43 369 reuss2 3356 nndi 6382 mulnqprl 7379 mulnqpru 7380 distrlem5prl 7397 distrlem5pru 7398 recexprlemss1l 7446 recexprlemss1u 7447 lemul12a 8623 nnmulcl 8744 elfz0fzfz0 9906 fzo1fzo0n0 9963 fzofzim 9968 elfzodifsumelfzo 9981 le2sq2 10371 oddprmgt2 11817 |
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