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Mirrors > Home > MPE Home > Th. List > Mathboxes > exlimii | Structured version Visualization version GIF version |
Description: Inference associated with exlimi 2210. Inferring a theorem when it is implied by an antecedent which may be true. (Contributed by BJ, 15-Sep-2018.) |
Ref | Expression |
---|---|
exlimii.1 | ⊢ Ⅎ𝑥𝜓 |
exlimii.2 | ⊢ (𝜑 → 𝜓) |
exlimii.3 | ⊢ ∃𝑥𝜑 |
Ref | Expression |
---|---|
exlimii | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimii.3 | . 2 ⊢ ∃𝑥𝜑 | |
2 | exlimii.1 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | exlimii.2 | . . 3 ⊢ (𝜑 → 𝜓) | |
4 | 2, 3 | exlimi 2210 | . 2 ⊢ (∃𝑥𝜑 → 𝜓) |
5 | 1, 4 | ax-mp 5 | 1 ⊢ 𝜓 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1782 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-ex 1783 df-nf 1787 |
This theorem is referenced by: exlimiieq1 35004 exlimiieq2 35005 |
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