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Theorem rgenzOLD 4049
 Description: Obsolete as of 22-Jul-2021. (Contributed by NM, 8-Dec-2012.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
rgenzOLD.1 ((𝐴 ≠ ∅ ∧ 𝑥𝐴) → 𝜑)
Assertion
Ref Expression
rgenzOLD 𝑥𝐴 𝜑
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem rgenzOLD
StepHypRef Expression
1 rzal 4045 . 2 (𝐴 = ∅ → ∀𝑥𝐴 𝜑)
2 rgenzOLD.1 . . 3 ((𝐴 ≠ ∅ ∧ 𝑥𝐴) → 𝜑)
32ralrimiva 2960 . 2 (𝐴 ≠ ∅ → ∀𝑥𝐴 𝜑)
41, 3pm2.61ine 2873 1 𝑥𝐴 𝜑
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 384   ∈ wcel 1987   ≠ wne 2790  ∀wral 2907  ∅c0 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-ral 2912  df-v 3188  df-dif 3558  df-nul 3892 This theorem is referenced by: (None)
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