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Theorem mo4OLD 2651
 Description: Obsolete version of mo4 2649 as of 18-Oct-2023. (Contributed by NM, 26-Jul-1995.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
mo4OLD.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
mo4OLD (∃*𝑥𝜑 ↔ ∀𝑥𝑦((𝜑𝜓) → 𝑥 = 𝑦))
Distinct variable groups:   𝑥,𝑦   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem mo4OLD
StepHypRef Expression
1 nfv 1915 . 2 𝑥𝜓
2 mo4OLD.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2mo4f 2650 1 (∃*𝑥𝜑 ↔ ∀𝑥𝑦((𝜑𝜓) → 𝑥 = 𝑦))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 208   ∧ wa 398  ∀wal 1535  ∃*wmo 2620 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2177 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-mo 2622 This theorem is referenced by: (None)
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