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Theorem 19.21-2 1554
 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 1472 . . 3 (y(φψ) ↔ (φyψ))
32albii 1356 . 2 (xy(φψ) ↔ x(φyψ))
4 19.21-2.1 . . 3 xφ
5419.21 1472 . 2 (x(φyψ) ↔ (φxyψ))
63, 5bitri 173 1 (xy(φψ) ↔ (φxyψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240  Ⅎwnf 1346 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347 This theorem is referenced by: (None)
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