Metamath Proof Explorer
Description: Inferring a theorem when it is implied by an equality which may be true.
(Contributed by BJ, 15-Sep-2018) (Revised by BJ, 30-Sep-2018)
|
|
Ref |
Expression |
|
Hypotheses |
exlimiieq2.1 |
⊢ Ⅎ 𝑦 𝜑 |
|
|
exlimiieq2.2 |
⊢ ( 𝑥 = 𝑦 → 𝜑 ) |
|
Assertion |
exlimiieq2 |
⊢ 𝜑 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
exlimiieq2.1 |
⊢ Ⅎ 𝑦 𝜑 |
2 |
|
exlimiieq2.2 |
⊢ ( 𝑥 = 𝑦 → 𝜑 ) |
3 |
|
ax6er |
⊢ ∃ 𝑦 𝑥 = 𝑦 |
4 |
1 2 3
|
exlimii |
⊢ 𝜑 |