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Theorem spsbce-2 38400
Description: Theorem *11.36 in [WhiteheadRussell] p. 162. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
spsbce-2 ([𝑧 / 𝑥][𝑤 / 𝑦]𝜑 → ∃𝑥𝑦𝜑)

Proof of Theorem spsbce-2
StepHypRef Expression
1 spsbe 1882 . 2 ([𝑧 / 𝑥][𝑤 / 𝑦]𝜑 → ∃𝑥[𝑤 / 𝑦]𝜑)
2 spsbe 1882 . . 3 ([𝑤 / 𝑦]𝜑 → ∃𝑦𝜑)
32eximi 1760 . 2 (∃𝑥[𝑤 / 𝑦]𝜑 → ∃𝑥𝑦𝜑)
41, 3syl 17 1 ([𝑧 / 𝑥][𝑤 / 𝑦]𝜑 → ∃𝑥𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1702  [wsb 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1703  df-sb 1879
This theorem is referenced by: (None)
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