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Theorem 19.23vv 1937
Description: Theorem 19.23v 1936 extended to two variables. (Contributed by NM, 10-Aug-2004.)
Assertion
Ref Expression
19.23vv (∀𝑥𝑦(𝜑𝜓) ↔ (∃𝑥𝑦𝜑𝜓))
Distinct variable groups:   𝜓,𝑥   𝜓,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem 19.23vv
StepHypRef Expression
1 19.23v 1936 . . 3 (∀𝑦(𝜑𝜓) ↔ (∃𝑦𝜑𝜓))
21albii 1813 . 2 (∀𝑥𝑦(𝜑𝜓) ↔ ∀𝑥(∃𝑦𝜑𝜓))
3 19.23v 1936 . 2 (∀𝑥(∃𝑦𝜑𝜓) ↔ (∃𝑥𝑦𝜑𝜓))
42, 3bitri 277 1 (∀𝑥𝑦(𝜑𝜓) ↔ (∃𝑥𝑦𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 208  wal 1528  wex 1773
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
This theorem depends on definitions:  df-bi 209  df-ex 1774
This theorem is referenced by:  ssrel  5650  ssrelrel  5662  raliunxp  5703  bnj1052  32235  bnj1030  32247
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