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Theorem 19.21-2 1864
Description: Theorem 19.21 of [Margaris] p. 90 but with 2 quantifiers. (Contributed by NM, 4-Feb-2005.)
Hypotheses
Ref Expression
19.21-2.1 xφ
19.21-2.2 yφ
Assertion
Ref Expression
19.21-2 (xy(φψ) ↔ (φxyψ))

Proof of Theorem 19.21-2
StepHypRef Expression
1 19.21-2.2 . . . 4 yφ
2119.21 1796 . . 3 (y(φψ) ↔ (φyψ))
32albii 1566 . 2 (xy(φψ) ↔ x(φyψ))
4 19.21-2.1 . . 3 xφ
5419.21 1796 . 2 (x(φyψ) ↔ (φxyψ))
63, 5bitri 240 1 (xy(φψ) ↔ (φxyψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  2eu6  2289
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