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Theorem r19.28av 2753
 Description: Restricted version of one direction of Theorem 19.28 of [Margaris] p. 90. (The other direction doesn't hold when A is empty.) (Contributed by NM, 2-Apr-2004.)
Assertion
Ref Expression
r19.28av ((φ x A ψ) → x A (φ ψ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.28av
StepHypRef Expression
1 r19.27av 2752 . 2 ((x A ψ φ) → x A (ψ φ))
2 ancom 437 . 2 ((φ x A ψ) ↔ (x A ψ φ))
3 ancom 437 . . 3 ((φ ψ) ↔ (ψ φ))
43ralbii 2638 . 2 (x A (φ ψ) ↔ x A (ψ φ))
51, 2, 43imtr4i 257 1 ((φ x A ψ) → x A (φ ψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  rr19.28v  2981  fununi  5160
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