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Mirrors > Home > MPE Home > Th. List > Mathboxes > in3an | Structured version Visualization version GIF version |
Description: The virtual deduction introduction rule converting the second conjunct of the third virtual hypothesis into the antecedent of the conclusion. exp4a 631 is the non-virtual deduction form of in3an 37857. (Contributed by Alan Sare, 25-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
in3an.1 | ⊢ ( 𝜑 , 𝜓 , (𝜒 ∧ 𝜃) ▶ 𝜏 ) |
Ref | Expression |
---|---|
in3an | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ (𝜃 → 𝜏) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | in3an.1 | . . . 4 ⊢ ( 𝜑 , 𝜓 , (𝜒 ∧ 𝜃) ▶ 𝜏 ) | |
2 | 1 | dfvd3i 37829 | . . 3 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
3 | 2 | exp4a 631 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
4 | 3 | dfvd3ir 37830 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ (𝜃 → 𝜏) ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ( wvd3 37824 |
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 df-vd3 37827 |
This theorem is referenced by: onfrALTlem2VD 38147 |
Copyright terms: Public domain | W3C validator |