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Mirrors > Home > MPE Home > Th. List > Mathboxes > exinst11 | Structured version Visualization version GIF version |
Description: Existential Instantiation. Virtual Deduction rule corresponding to a special case of the Natural Deduction Sequent Calculus rule called Rule C in [Margaris] p. 79 and E ∃ in Table 1 on page 4 of the paper "Extracting information from intermediate T-systems" (2000) presented at IMLA99 by Mauro Ferrari, Camillo Fiorentini, and Pierangelo Miglioli. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
exinst11.1 | ⊢ ( 𝜑 ▶ ∃𝑥𝜓 ) |
exinst11.2 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
exinst11.3 | ⊢ (𝜑 → ∀𝑥𝜑) |
exinst11.4 | ⊢ (𝜒 → ∀𝑥𝜒) |
Ref | Expression |
---|---|
exinst11 | ⊢ ( 𝜑 ▶ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exinst11.1 | . . . 4 ⊢ ( 𝜑 ▶ ∃𝑥𝜓 ) | |
2 | 1 | in1 40782 | . . 3 ⊢ (𝜑 → ∃𝑥𝜓) |
3 | exinst11.2 | . . . 4 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
4 | 3 | dfvd2i 40796 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) |
5 | exinst11.3 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
6 | exinst11.4 | . . 3 ⊢ (𝜒 → ∀𝑥𝜒) | |
7 | 2, 4, 5, 6 | eexinst11 40738 | . 2 ⊢ (𝜑 → 𝜒) |
8 | 7 | dfvd1ir 40784 | 1 ⊢ ( 𝜑 ▶ 𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1526 ∃wex 1771 ( wvd1 40780 ( wvd2 40788 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-nf 1776 df-vd1 40781 df-vd2 40789 |
This theorem is referenced by: vk15.4jVD 41125 |
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