Description: Obsolete version of reuanid as of 12-Jan-2025. (Contributed by Peter Mazsa, 12-Feb-2018) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | reuanidOLD | ⊢ ( ∃! 𝑥 ∈ 𝐴 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ↔ ∃! 𝑥 ∈ 𝐴 𝜑 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anabs5 | ⊢ ( ( 𝑥 ∈ 𝐴 ∧ ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ) ↔ ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ) | |
| 2 | 1 | eubii | ⊢ ( ∃! 𝑥 ( 𝑥 ∈ 𝐴 ∧ ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ) ↔ ∃! 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ) |
| 3 | df-reu | ⊢ ( ∃! 𝑥 ∈ 𝐴 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ↔ ∃! 𝑥 ( 𝑥 ∈ 𝐴 ∧ ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ) ) | |
| 4 | df-reu | ⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ∃! 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ) | |
| 5 | 2 3 4 | 3bitr4i | ⊢ ( ∃! 𝑥 ∈ 𝐴 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) ↔ ∃! 𝑥 ∈ 𝐴 𝜑 ) |