Theorem reubidvaOLD 3348

Description: Obsolete version of reubidva 3347 as of 14-Jan-2023. (Contributed by NM, 13-Nov-2004.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
reubidvaOLD.1	⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → (𝜓 ↔ 𝜒))

Assertion

Ref	Expression
reubidvaOLD	⊢ (𝜑 → (∃!𝑥 ∈ 𝐴 𝜓 ↔ ∃!𝑥 ∈ 𝐴 𝜒))

Distinct variable group:   𝜑,𝑥

Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem reubidvaOLD

Step	Hyp	Ref	Expression
1		nfv 1892	. 2 ⊢ Ⅎ𝑥𝜑
2		reubidvaOLD.1	. 2 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → (𝜓 ↔ 𝜒))
3	1, 2	reubida 3346	1 ⊢ (𝜑 → (∃!𝑥 ∈ 𝐴 𝜓 ↔ ∃!𝑥 ∈ 𝐴 𝜒))

Syntax hints:   → wi 4   ↔ wb 207   ∧ wa 396   ∈ wcel 2081  ∃!wreu 3107

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-12 2141

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1762  df-nf 1766  df-mo 2576  df-eu 2612  df-reu 3112

This theorem is referenced by: (None)