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Mirrors > Home > MPE Home > Th. List > Mathboxes > gen31 | Structured version Visualization version GIF version |
Description: Virtual deduction generalizing rule for one quantifying variable and three virtual hypothesis. gen31 37867 is ggen31 37781 with virtual deductions. (Contributed by Alan Sare, 22-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
gen31.1 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
Ref | Expression |
---|---|
gen31 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ ∀𝑥𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen31.1 | . . . 4 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) | |
2 | 1 | dfvd3i 37829 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | ggen31 37781 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → ∀𝑥𝜃))) |
4 | 3 | dfvd3ir 37830 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ ∀𝑥𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1473 ( wvd3 37824 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 |
This theorem depends on definitions: df-bi 196 df-an 385 df-3an 1033 df-vd3 37827 |
This theorem is referenced by: onfrALTlem2VD 38147 |
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