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Mirrors > Home > MPE Home > Th. List > exlimih | Structured version Visualization version GIF version |
Description: Inference associated with 19.23 2067. See exlimiv 1845 for a version with a dv condition requiring fewer axioms. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) |
Ref | Expression |
---|---|
exlimih.1 | ⊢ (𝜓 → ∀𝑥𝜓) |
exlimih.2 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
exlimih | ⊢ (∃𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimih.1 | . . 3 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | 1 | nf5i 2011 | . 2 ⊢ Ⅎ𝑥𝜓 |
3 | exlimih.2 | . 2 ⊢ (𝜑 → 𝜓) | |
4 | 2, 3 | exlimi 2073 | 1 ⊢ (∃𝑥𝜑 → 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 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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