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Mirrors > Home > MPE Home > Th. List > 19.35ri | Structured version Visualization version GIF version |
Description: Inference associated with 19.35 1794. (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 1794 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓)) | |
3 | 1, 2 | mpbir 220 | 1 ⊢ ∃𝑥(𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ∃wex 1695 |
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-ex 1696 |
This theorem is referenced by: qexmid 2051 axrep1 4700 axextnd 9292 axinfnd 9307 bj-axrep1 31976 |
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