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Metamath Proof Explorer
Description: Formula-building rule for two existential quantifiers (deduction form).
(Contributed by NM, 1-May-1995)
|
|
Ref |
Expression |
|
Hypothesis |
2albidv.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
Assertion |
2exbidv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 ↔ ∃ 𝑥 ∃ 𝑦 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
2albidv.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
| 2 |
1
|
exbidv |
⊢ ( 𝜑 → ( ∃ 𝑦 𝜓 ↔ ∃ 𝑦 𝜒 ) ) |
| 3 |
2
|
exbidv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 ↔ ∃ 𝑥 ∃ 𝑦 𝜒 ) ) |