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Theorem eqrdOLD 3772
 Description: Obsolete proof of eqrd 3771 as of 1-Dec-2021. (Contributed by Thierry Arnoux, 21-Mar-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eqrd.0 𝑥𝜑
eqrd.1 𝑥𝐴
eqrd.2 𝑥𝐵
eqrd.3 (𝜑 → (𝑥𝐴𝑥𝐵))
Assertion
Ref Expression
eqrdOLD (𝜑𝐴 = 𝐵)

Proof of Theorem eqrdOLD
StepHypRef Expression
1 eqrd.0 . . 3 𝑥𝜑
2 eqrd.1 . . 3 𝑥𝐴
3 eqrd.2 . . 3 𝑥𝐵
4 eqrd.3 . . . 4 (𝜑 → (𝑥𝐴𝑥𝐵))
54biimpd 219 . . 3 (𝜑 → (𝑥𝐴𝑥𝐵))
61, 2, 3, 5ssrd 3757 . 2 (𝜑𝐴𝐵)
74biimprd 238 . . 3 (𝜑 → (𝑥𝐵𝑥𝐴))
81, 3, 2, 7ssrd 3757 . 2 (𝜑𝐵𝐴)
96, 8eqssd 3769 1 (𝜑𝐴 = 𝐵)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   = wceq 1631  Ⅎwnf 1856   ∈ wcel 2145  Ⅎwnfc 2900 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-in 3730  df-ss 3737 This theorem is referenced by: (None)
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