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Theorem axc16nfOLD 2339
Description: Obsolete proof of axc16nf 2316 as of 12-Oct-2021. (Contributed by Mario Carneiro, 7-Oct-2016.) Remove dependency on ax-11 2202. (Revised by Wolf Lammen, 9-Sep-2018.) (Proof shortened by BJ, 14-Jun-2019.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
axc16nfOLD (∀𝑥 𝑥 = 𝑦 → Ⅎ𝑧𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧)

Proof of Theorem axc16nfOLD
Dummy variable 𝑤 is distinct from all other variables.
StepHypRef Expression
1 aev 2152 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧 𝑧 = 𝑤)
2 nfa1 2196 . . 3 𝑧𝑧 𝑧 = 𝑤
3 axc16 2314 . . 3 (∀𝑧 𝑧 = 𝑤 → (𝜑 → ∀𝑧𝜑))
42, 3nf5d 2295 . 2 (∀𝑧 𝑧 = 𝑤 → Ⅎ𝑧𝜑)
51, 4syl 17 1 (∀𝑥 𝑥 = 𝑦 → Ⅎ𝑧𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1635  wnf 1863
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-10 2186  ax-12 2215
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-ex 1860  df-nf 1864
This theorem is referenced by: (None)
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