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Theorem r19.26m 2438
 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 1367 . 2 (x((x Aφ) (x Bψ)) ↔ (x(x Aφ) x(x Bψ)))
2 df-ral 2305 . . 3 (x A φx(x Aφ))
3 df-ral 2305 . . 3 (x B ψx(x Bψ))
42, 3anbi12i 433 . 2 ((x A φ x B ψ) ↔ (x(x Aφ) x(x Bψ)))
51, 4bitr4i 176 1 (x((x Aφ) (x Bψ)) ↔ (x A φ x B ψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98  ∀wal 1240   ∈ wcel 1390  ∀wral 2300 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 This theorem depends on definitions:  df-bi 110  df-ral 2305 This theorem is referenced by: (None)
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