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Theorem dveel2ALT 36062
 Description: Alternate proof of dveel2 2478 using ax-c16 36015 instead of ax-5 1904. (Contributed by NM, 10-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveel2ALT (¬ ∀𝑥 𝑥 = 𝑦 → (𝑧𝑦 → ∀𝑥 𝑧𝑦))
Distinct variable group:   𝑥,𝑧

Proof of Theorem dveel2ALT
Dummy variable 𝑤 is distinct from all other variables.
StepHypRef Expression
1 ax5el 36060 . 2 (𝑧𝑤 → ∀𝑥 𝑧𝑤)
2 ax5el 36060 . 2 (𝑧𝑦 → ∀𝑤 𝑧𝑦)
3 elequ2 2122 . 2 (𝑤 = 𝑦 → (𝑧𝑤𝑧𝑦))
41, 2, 3dvelimh 2465 1 (¬ ∀𝑥 𝑥 = 𝑦 → (𝑧𝑦 → ∀𝑥 𝑧𝑦))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1528 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-13 2383  ax-c14 36014  ax-c16 36015 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778 This theorem is referenced by: (None)
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