New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  19.23hOLD GIF version

Theorem 19.23hOLD 1820
 Description: Obsolete proof of 19.23h 1802 as of 1-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.23hOLD.1 (ψxψ)
Assertion
Ref Expression
19.23hOLD (x(φψ) ↔ (xφψ))

Proof of Theorem 19.23hOLD
StepHypRef Expression
1 exim 1575 . . 3 (x(φψ) → (xφxψ))
2 19.23hOLD.1 . . . 4 (ψxψ)
3219.9h 1780 . . 3 (xψψ)
41, 3syl6ib 217 . 2 (x(φψ) → (xφψ))
5 hbe1 1731 . . . 4 (xφxxφ)
65, 2hbim 1817 . . 3 ((xφψ) → x(xφψ))
7 19.8a 1756 . . . 4 (φxφ)
87imim1i 54 . . 3 ((xφψ) → (φψ))
96, 8alrimih 1565 . 2 ((xφψ) → x(φψ))
104, 9impbii 180 1 (x(φψ) ↔ (xφψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀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  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)
 Copyright terms: Public domain W3C validator