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Theorem r19.29r 2755
 Description: Variation of Theorem 19.29 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
r19.29r ((x A φ x A ψ) → x A (φ ψ))

Proof of Theorem r19.29r
StepHypRef Expression
1 r19.29 2754 . 2 ((x A ψ x A φ) → x A (ψ φ))
2 ancom 437 . 2 ((x A φ x A ψ) ↔ (x A ψ x A φ))
3 ancom 437 . . 3 ((φ ψ) ↔ (ψ φ))
43rexbii 2639 . 2 (x A (φ ψ) ↔ x A (ψ φ))
51, 2, 43imtr4i 257 1 ((x A φ x A ψ) → x A (φ ψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wral 2614  ∃wrex 2615 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-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  df-rex 2620 This theorem is referenced by:  2reu5  3044
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