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Theorem nfaldOLD 1853
 Description: Obsolete proof of nfald 1852 as of 6-Jan-2018. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfald.1 yφ
nfald.2 (φ → Ⅎxψ)
Assertion
Ref Expression
nfaldOLD (φ → Ⅎxyψ)

Proof of Theorem nfaldOLD
StepHypRef Expression
1 nfald.1 . . 3 yφ
2 nfald.2 . . 3 (φ → Ⅎxψ)
31, 2alrimi 1765 . 2 (φyxψ)
4 nfnf1 1790 . . . 4 xxψ
54nfal 1842 . . 3 xyxψ
6 nfr 1761 . . . . 5 (Ⅎxψ → (ψxψ))
76al2imi 1561 . . . 4 (yxψ → (yψyxψ))
8 ax-7 1734 . . . 4 (yxψxyψ)
97, 8syl6 29 . . 3 (yxψ → (yψxyψ))
105, 9nfd 1766 . 2 (yxψ → Ⅎxyψ)
113, 10syl 15 1 (φ → Ⅎxyψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544 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-7 1734  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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