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Mirrors > Home > MPE Home > Th. List > pm3.2an3OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of pm3.2an3 1233 as of 24-Apr-2021. (Contributed by Alan Sare, 24-Oct-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pm3.2an3OLD | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜑 ∧ 𝜓 ∧ 𝜒)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2 462 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → ((𝜑 ∧ 𝜓) ∧ 𝜒))) | |
2 | 1 | ex 449 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → ((𝜑 ∧ 𝜓) ∧ 𝜒)))) |
3 | df-3an 1033 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒)) | |
4 | 3 | bicomi 213 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) |
5 | 2, 4 | syl8ib 245 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜑 ∧ 𝜓 ∧ 𝜒)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 df-3an 1033 |
This theorem is referenced by: (None) |
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