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Mirrors > Home > MPE Home > Th. List > 19.35ri | Structured version Visualization version GIF version |
Description: Inference associated with 19.35 1805. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
19.35ri.1 | ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) |
Ref | Expression |
---|---|
19.35ri | ⊢ ∃𝑥(𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.35ri.1 | . 2 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) | |
2 | 19.35 1805 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓)) | |
3 | 1, 2 | mpbir 221 | 1 ⊢ ∃𝑥(𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-ex 1705 |
This theorem is referenced by: qexmid 2063 axrep1 4772 axextnd 9413 axinfnd 9428 bj-axrep1 32788 |
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