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Mirrors > Home > ILE Home > Th. List > a1dd | GIF version |
Description: Deduction introducing a nested embedded antecedent. (Contributed by NM, 17-Dec-2004.) (Proof shortened by O'Cat, 15-Jan-2008.) |
Ref | Expression |
---|---|
a1dd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
a1dd | ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a1dd.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | ax-1 6 | . 2 ⊢ (𝜒 → (𝜃 → 𝜒)) | |
3 | 1, 2 | syl6 33 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: exmidsssnc 4134 nnsub 8783 difelfzle 9942 facdiv 10516 facwordi 10518 faclbnd 10519 dvdsabseq 11581 divgcdcoprm0 11818 exprmfct 11854 prmfac1 11866 bj-inf2vnlem2 13340 |
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