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Theorem nfcrALT 2966
 Description: Alternate version of nfcr 2965. Avoids ax-8 2116 but uses ax-12 2178. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
nfcrALT (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
Distinct variable groups:   𝑥,𝑦   𝑦,𝐴
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfcrALT
StepHypRef Expression
1 df-nfc 2962 . 2 (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
2 sp 2183 . 2 (∀𝑦𝑥 𝑦𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2sylbi 220 1 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  Ⅎwnf 1785   ∈ wcel 2114  Ⅎwnfc 2960 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2178 This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nfc 2962 This theorem is referenced by: (None)
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