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Mirrors > Home > MPE Home > Th. List > Mathboxes > in2an | Structured version Visualization version GIF version |
Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. expd 451 is the non-virtual deduction form of in2an 37854. (Contributed by Alan Sare, 30-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
in2an.1 | ⊢ ( 𝜑 , (𝜓 ∧ 𝜒) ▶ 𝜃 ) |
Ref | Expression |
---|---|
in2an | ⊢ ( 𝜑 , 𝜓 ▶ (𝜒 → 𝜃) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | in2an.1 | . . . 4 ⊢ ( 𝜑 , (𝜓 ∧ 𝜒) ▶ 𝜃 ) | |
2 | 1 | dfvd2i 37822 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
3 | 2 | expd 451 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
4 | 3 | dfvd2ir 37823 | 1 ⊢ ( 𝜑 , 𝜓 ▶ (𝜒 → 𝜃) ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ( wvd2 37814 |
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-vd2 37815 |
This theorem is referenced by: onfrALTVD 38149 |
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