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Theorem 19.32 1875
 Description: Theorem 19.32 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.32.1 xφ
Assertion
Ref Expression
19.32 (x(φ ψ) ↔ (φ xψ))

Proof of Theorem 19.32
StepHypRef Expression
1 19.32.1 . . . 4 xφ
21nfn 1793 . . 3 x ¬ φ
3219.21 1796 . 2 (xφψ) ↔ (¬ φxψ))
4 df-or 359 . . 3 ((φ ψ) ↔ (¬ φψ))
54albii 1566 . 2 (x(φ ψ) ↔ xφψ))
6 df-or 359 . 2 ((φ xψ) ↔ (¬ φxψ))
73, 5, 63bitr4i 268 1 (x(φ ψ) ↔ (φ xψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357  ∀wal 1540  Ⅎwnf 1544 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-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-or 359  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  19.31  1876  2eu3  2286  axi12  2333
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