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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 2383 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
4 | 1, 2, 3 | exlimii 35001 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 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 ax-13 2372 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1783 df-nf 1787 |
This theorem is referenced by: (None) |
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