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Mirrors > Home > ILE Home > Th. List > 19.36i | GIF version |
Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.) |
Ref | Expression |
---|---|
19.36i.1 | ⊢ Ⅎ𝑥𝜓 |
19.36i.2 | ⊢ ∃𝑥(𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.36i | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.36i.2 | . . 3 ⊢ ∃𝑥(𝜑 → 𝜓) | |
2 | 1 | 19.35i 1625 | . 2 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) |
3 | 19.36i.1 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
4 | id 19 | . . 3 ⊢ (𝜓 → 𝜓) | |
5 | 3, 4 | exlimi 1594 | . 2 ⊢ (∃𝑥𝜓 → 𝜓) |
6 | 2, 5 | syl 14 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1351 Ⅎwnf 1460 ∃wex 1492 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-nf 1461 |
This theorem is referenced by: spimfv 1699 19.36aiv 1901 vtoclf 2790 |
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