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Theorem sbfALT 2570
 Description: Alternate version of sbf 2268. (Contributed by NM, 14-May-1993.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
dfsb1.ph (𝜃 ↔ ((𝑥 = 𝑦𝜑) ∧ ∃𝑥(𝑥 = 𝑦𝜑)))
sbfALT.1 𝑥𝜑
Assertion
Ref Expression
sbfALT (𝜃𝜑)

Proof of Theorem sbfALT
StepHypRef Expression
1 sbfALT.1 . 2 𝑥𝜑
2 dfsb1.ph . . 3 (𝜃 ↔ ((𝑥 = 𝑦𝜑) ∧ ∃𝑥(𝑥 = 𝑦𝜑)))
32sbftALT 2569 . 2 (Ⅎ𝑥𝜑 → (𝜃𝜑))
41, 3ax-mp 5 1 (𝜃𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   ∧ wa 399  ∃wex 1781  Ⅎwnf 1785 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 2175  ax-13 2379 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786 This theorem is referenced by:  sbrimALT  2585  sbieALT  2589
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