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Mirrors > Home > MPE Home > Th. List > 2a1dd | Structured version Visualization version GIF version |
Description: Double deduction introducing two antecedents. Two applications of 2a1dd 51. Deduction associated with 2a1d 26. Double deduction associated with 2a1 28 and 2a1i 12. (Contributed by Jeff Hankins, 5-Aug-2009.) |
Ref | Expression |
---|---|
2a1dd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
2a1dd | ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → 𝜒)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2a1dd.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | a1dd 50 | . 2 ⊢ (𝜑 → (𝜓 → (𝜏 → 𝜒))) |
3 | 2 | a1dd 50 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → 𝜒)))) |
Colors of variables: wff setvar 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: nnsub 11675 |
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