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Mirrors > Home > MPE Home > Th. List > Mathboxes > gen11nv | Structured version Visualization version GIF version |
Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis without distinct variables. alrimih 1815 is gen11nv 40828 without virtual deductions. (Contributed by Alan Sare, 12-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
gen11nv.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
gen11nv.2 | ⊢ ( 𝜑 ▶ 𝜓 ) |
Ref | Expression |
---|---|
gen11nv | ⊢ ( 𝜑 ▶ ∀𝑥𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen11nv.1 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | gen11nv.2 | . . . 4 ⊢ ( 𝜑 ▶ 𝜓 ) | |
3 | 2 | in1 40782 | . . 3 ⊢ (𝜑 → 𝜓) |
4 | 1, 3 | alrimih 1815 | . 2 ⊢ (𝜑 → ∀𝑥𝜓) |
5 | 4 | dfvd1ir 40784 | 1 ⊢ ( 𝜑 ▶ ∀𝑥𝜓 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1526 ( wvd1 40780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 |
This theorem depends on definitions: df-bi 208 df-vd1 40781 |
This theorem is referenced by: tratrbVD 41072 hbimpgVD 41115 hbalgVD 41116 hbexgVD 41117 e2ebindVD 41123 |
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