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Mirrors > Home > MPE Home > Th. List > ex-natded5.2i | Structured version Visualization version GIF version |
Description: The same as ex-natded5.2 27875 and ex-natded5.2-2 27876 but with no context. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ex-natded5.2i.1 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
ex-natded5.2i.2 | ⊢ (𝜒 → 𝜓) |
ex-natded5.2i.3 | ⊢ 𝜒 |
Ref | Expression |
---|---|
ex-natded5.2i | ⊢ 𝜃 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ex-natded5.2i.3 | . . . 4 ⊢ 𝜒 | |
2 | ex-natded5.2i.2 | . . . 4 ⊢ (𝜒 → 𝜓) | |
3 | 1, 2 | ax-mp 5 | . . 3 ⊢ 𝜓 |
4 | 3, 1 | pm3.2i 471 | . 2 ⊢ (𝜓 ∧ 𝜒) |
5 | ex-natded5.2i.1 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
6 | 4, 5 | ax-mp 5 | 1 ⊢ 𝜃 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
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 208 df-an 397 |
This theorem is referenced by: (None) |
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