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Theorem 19.43OLD 1606
 Description: Obsolete proof of 19.43 1605 as of 3-May-2016. Leave this in for the example on the mmrecent.html page. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.43OLD (x(φ ψ) ↔ (xφ xψ))

Proof of Theorem 19.43OLD
StepHypRef Expression
1 ioran 476 . . . . 5 (¬ (φ ψ) ↔ (¬ φ ¬ ψ))
21albii 1566 . . . 4 (x ¬ (φ ψ) ↔ xφ ¬ ψ))
3 19.26 1593 . . . 4 (xφ ¬ ψ) ↔ (x ¬ φ x ¬ ψ))
4 alnex 1543 . . . . 5 (x ¬ φ ↔ ¬ xφ)
5 alnex 1543 . . . . 5 (x ¬ ψ ↔ ¬ xψ)
64, 5anbi12i 678 . . . 4 ((x ¬ φ x ¬ ψ) ↔ (¬ xφ ¬ xψ))
72, 3, 63bitri 262 . . 3 (x ¬ (φ ψ) ↔ (¬ xφ ¬ xψ))
87notbii 287 . 2 x ¬ (φ ψ) ↔ ¬ (¬ xφ ¬ xψ))
9 df-ex 1542 . 2 (x(φ ψ) ↔ ¬ x ¬ (φ ψ))
10 oran 482 . 2 ((xφ xψ) ↔ ¬ (¬ xφ ¬ xψ))
118, 9, 103bitr4i 268 1 (x(φ ψ) ↔ (xφ xψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 176   ∨ wo 357   ∧ wa 358  ∀wal 1540  ∃wex 1541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1542 This theorem is referenced by: (None)
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