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Theorem 19.23tOLD 1819
 Description: Obsolete proof of 19.23t 1800 as of 1-Jan-2018. (Contributed by NM, 7-Nov-2005.) (New usage is discouraged.)
Assertion
Ref Expression
19.23tOLD (Ⅎxψ → (x(φψ) ↔ (xφψ)))

Proof of Theorem 19.23tOLD
StepHypRef Expression
1 exim 1575 . . 3 (x(φψ) → (xφxψ))
2 19.9t 1779 . . . 4 (Ⅎxψ → (xψψ))
32imbi2d 307 . . 3 (Ⅎxψ → ((xφxψ) ↔ (xφψ)))
41, 3syl5ib 210 . 2 (Ⅎxψ → (x(φψ) → (xφψ)))
5 nfnf1 1790 . . 3 xxψ
6 nfe1 1732 . . . . 5 xxφ
76a1i 10 . . . 4 (Ⅎxψ → Ⅎxxφ)
8 id 19 . . . 4 (Ⅎxψ → Ⅎxψ)
97, 8nfimd 1808 . . 3 (Ⅎxψ → Ⅎx(xφψ))
10 19.8a 1756 . . . . 5 (φxφ)
1110a1i 10 . . . 4 (Ⅎxψ → (φxφ))
1211imim1d 69 . . 3 (Ⅎxψ → ((xφψ) → (φψ)))
135, 9, 12alrimdd 1768 . 2 (Ⅎxψ → ((xφψ) → x(φψ)))
144, 13impbid 183 1 (Ⅎxψ → (x(φψ) ↔ (xφψ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541  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-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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