Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reubidvaOLD Structured version   Visualization version   GIF version

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 ((𝜑𝑥𝐴) → (𝜓𝜒))
Assertion
Ref Expression
reubidvaOLD (𝜑 → (∃!𝑥𝐴 𝜓 ↔ ∃!𝑥𝐴 𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem reubidvaOLD
StepHypRef Expression
1 nfv 1892 . 2 𝑥𝜑
2 reubidvaOLD.1 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
31, 2reubida 3346 1 (𝜑 → (∃!𝑥𝐴 𝜓 ↔ ∃!𝑥𝐴 𝜒))
 Colors of variables: wff setvar class 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)
 Copyright terms: Public domain W3C validator