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Mirrors > Home > MPE Home > Th. List > Mathboxes > exlimiieq1 | Structured version Visualization version GIF version |
Description: Inferring a theorem when it is implied by an equality which may be true. (Contributed by BJ, 30-Sep-2018.) |
Ref | Expression |
---|---|
exlimiieq1.1 | ⊢ Ⅎ𝑥𝜑 |
exlimiieq1.2 | ⊢ (𝑥 = 𝑦 → 𝜑) |
Ref | Expression |
---|---|
exlimiieq1 | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimiieq1.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | exlimiieq1.2 | . 2 ⊢ (𝑥 = 𝑦 → 𝜑) | |
3 | ax6e 2238 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
4 | 1, 2, 3 | exlimii 32006 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Ⅎwnf 1699 |
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-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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