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Metamath Proof Explorer
Description: Version of equs4v with its consequence simplified by exsimpr .
(Contributed by BJ, 9-Nov-2021)
|
|
Ref |
Expression |
|
Assertion |
alequexv |
⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → ∃ 𝑥 𝜑 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ax6ev |
⊢ ∃ 𝑥 𝑥 = 𝑦 |
| 2 |
|
exim |
⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → ( ∃ 𝑥 𝑥 = 𝑦 → ∃ 𝑥 𝜑 ) ) |
| 3 |
1 2
|
mpi |
⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → ∃ 𝑥 𝜑 ) |