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Mirrors > Home > MPE Home > Th. List > Mathboxes > exinst01 | 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 |
---|---|
exinst01.1 | ⊢ ∃𝑥𝜓 |
exinst01.2 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
exinst01.3 | ⊢ (𝜑 → ∀𝑥𝜑) |
exinst01.4 | ⊢ (𝜒 → ∀𝑥𝜒) |
Ref | Expression |
---|---|
exinst01 | ⊢ ( 𝜑 ▶ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exinst01.1 | . . 3 ⊢ ∃𝑥𝜓 | |
2 | exinst01.2 | . . . 4 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
3 | 2 | dfvd2i 44497 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) |
4 | exinst01.3 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
5 | exinst01.4 | . . 3 ⊢ (𝜒 → ∀𝑥𝜒) | |
6 | 1, 3, 4, 5 | eexinst01 44438 | . 2 ⊢ (𝜑 → 𝜒) |
7 | 6 | dfvd1ir 44485 | 1 ⊢ ( 𝜑 ▶ 𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1535 ∃wex 1777 ( wvd1 44481 ( wvd2 44489 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-10 2136 ax-12 2173 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1778 df-nf 1782 df-vd1 44482 df-vd2 44490 |
This theorem is referenced by: vk15.4jVD 44826 |
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