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Mirrors > Home > MPE Home > Th. List > Mathboxes > ggen31 | Structured version Visualization version GIF version |
Description: gen31 37867 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ggen31.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
ggen31 | ⊢ (𝜑 → (𝜓 → (𝜒 → ∀𝑥𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ggen31.1 | . . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | 1 | imp 444 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
3 | 2 | alrimdv 1844 | . 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → ∀𝑥𝜃)) |
4 | 3 | ex 449 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → ∀𝑥𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∀wal 1473 |
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 |
This theorem is referenced by: onfrALTlem2 37782 gen31 37867 |
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