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Theorem 19.26-3an 1595
 Description: Theorem 19.26 of [Margaris] p. 90 with triple conjunction. (Contributed by NM, 13-Sep-2011.)
Assertion
Ref Expression
19.26-3an (x(φ ψ χ) ↔ (xφ xψ xχ))

Proof of Theorem 19.26-3an
StepHypRef Expression
1 19.26 1593 . . 3 (x((φ ψ) χ) ↔ (x(φ ψ) xχ))
2 19.26 1593 . . . 4 (x(φ ψ) ↔ (xφ xψ))
32anbi1i 676 . . 3 ((x(φ ψ) xχ) ↔ ((xφ xψ) xχ))
41, 3bitri 240 . 2 (x((φ ψ) χ) ↔ ((xφ xψ) xχ))
5 df-3an 936 . . 3 ((φ ψ χ) ↔ ((φ ψ) χ))
65albii 1566 . 2 (x(φ ψ χ) ↔ x((φ ψ) χ))
7 df-3an 936 . 2 ((xφ xψ xχ) ↔ ((xφ xψ) xχ))
84, 6, 73bitr4i 268 1 (x(φ ψ χ) ↔ (xφ xψ xχ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358   ∧ w3a 934  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936 This theorem is referenced by: (None)
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