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Theorem dveeq2ALT 2476
Description: Alternate proof of dveeq2 2396, shorter but requiring ax-11 2161. (Contributed by NM, 2-Jan-2002.) (Revised by NM, 20-Jul-2015.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
dveeq2ALT (¬ ∀𝑥 𝑥 = 𝑦 → (𝑧 = 𝑦 → ∀𝑥 𝑧 = 𝑦))
Distinct variable group:   𝑥,𝑧

Proof of Theorem dveeq2ALT
Dummy variable 𝑤 is distinct from all other variables.
StepHypRef Expression
1 equequ2 2033 . 2 (𝑤 = 𝑦 → (𝑧 = 𝑤𝑧 = 𝑦))
21dvelimv 2474 1 (¬ ∀𝑥 𝑥 = 𝑦 → (𝑧 = 𝑦 → ∀𝑥 𝑧 = 𝑦))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1535
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  ax-13 2390
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785
This theorem is referenced by: (None)
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