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Theorem 19.23vv 1905
 Description: Theorem 19.23v 1904 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 1904 . . 3 (∀𝑦(𝜑𝜓) ↔ (∃𝑦𝜑𝜓))
21albii 1744 . 2 (∀𝑥𝑦(𝜑𝜓) ↔ ∀𝑥(∃𝑦𝜑𝜓))
3 19.23v 1904 . 2 (∀𝑥(∃𝑦𝜑𝜓) ↔ (∃𝑥𝑦𝜑𝜓))
42, 3bitri 264 1 (∀𝑥𝑦(𝜑𝜓) ↔ (∃𝑥𝑦𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1478  ∃wex 1701 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890 This theorem depends on definitions:  df-bi 197  df-ex 1702 This theorem is referenced by:  ssrel  5173  ssrelOLD  5174  ssrelrel  5186  raliunxp  5226  bnj1052  30743  bnj1030  30755
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