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Mirrors > Home > MPE Home > Th. List > ex-natded5.3i | Structured version Visualization version GIF version |
Description: The same as ex-natded5.3 27591 and ex-natded5.3-2 27592 but with no context. Identical to jccir 513, which should be used instead. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ex-natded5.3i.1 | ⊢ (𝜓 → 𝜒) |
ex-natded5.3i.2 | ⊢ (𝜒 → 𝜃) |
Ref | Expression |
---|---|
ex-natded5.3i | ⊢ (𝜓 → (𝜒 ∧ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ex-natded5.3i.1 | . 2 ⊢ (𝜓 → 𝜒) | |
2 | ex-natded5.3i.2 | . . 3 ⊢ (𝜒 → 𝜃) | |
3 | 1, 2 | syl 17 | . 2 ⊢ (𝜓 → 𝜃) |
4 | 1, 3 | jca 503 | 1 ⊢ (𝜓 → (𝜒 ∧ 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 |
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 198 df-an 385 |
This theorem is referenced by: (None) |
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