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Mirrors > Home > MPE Home > Th. List > Mathboxes > gen21nv | Structured version Visualization version GIF version |
Description: Virtual deduction form of alrimdh 1777. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
gen21nv.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
gen21nv.2 | ⊢ (𝜓 → ∀𝑥𝜓) |
gen21nv.3 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
Ref | Expression |
---|---|
gen21nv | ⊢ ( 𝜑 , 𝜓 ▶ ∀𝑥𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen21nv.1 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | gen21nv.2 | . . 3 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | gen21nv.3 | . . . 4 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
4 | 3 | dfvd2i 37822 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) |
5 | 1, 2, 4 | alrimdh 1777 | . 2 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
6 | 5 | dfvd2ir 37823 | 1 ⊢ ( 𝜑 , 𝜓 ▶ ∀𝑥𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ( wvd2 37814 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-an 385 df-vd2 37815 |
This theorem is referenced by: ssralv2VD 38124 |
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