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Theorem 19.21hOLD 1840
 Description: Obsolete proof of 19.21h 1797 as of 1-Jan-2018. (Contributed by NM, 1-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.21hOLD.1 (φxφ)
Assertion
Ref Expression
19.21hOLD (x(φψ) ↔ (φxψ))

Proof of Theorem 19.21hOLD
StepHypRef Expression
1 19.21hOLD.1 . . 3 (φxφ)
2 alim 1558 . . 3 (x(φψ) → (xφxψ))
31, 2syl5 28 . 2 (x(φψ) → (φxψ))
4 hba1 1786 . . . 4 (xψxxψ)
51, 4hbim 1817 . . 3 ((φxψ) → x(φxψ))
6 sp 1747 . . . 4 (xψψ)
76imim2i 13 . . 3 ((φxψ) → (φψ))
85, 7alrimih 1565 . 2 ((φxψ) → x(φψ))
93, 8impbii 180 1 (x(φψ) ↔ (φxψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540 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)
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