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Theorem r19.26m 2749
Description: Theorem 19.26 of [Margaris] p. 90 with mixed quantifiers. (Contributed by NM, 22-Feb-2004.)
Assertion
Ref Expression
r19.26m (x((x Aφ) (x Bψ)) ↔ (x A φ x B ψ))

Proof of Theorem r19.26m
StepHypRef Expression
1 19.26 1593 . 2 (x((x Aφ) (x Bψ)) ↔ (x(x Aφ) x(x Bψ)))
2 df-ral 2619 . . 3 (x A φx(x Aφ))
3 df-ral 2619 . . 3 (x B ψx(x Bψ))
42, 3anbi12i 678 . 2 ((x A φ x B ψ) ↔ (x(x Aφ) x(x Bψ)))
51, 4bitr4i 243 1 (x((x Aφ) (x Bψ)) ↔ (x A φ x B ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358  wal 1540   wcel 1710  wral 2614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ral 2619
This theorem is referenced by: (None)
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