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Theorem cbv3hvOLD 1851
 Description: Obsolete proof of cbv3hv 1850 as of 29-Dec-2017. (Contributed by NM, 25-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
cbv3hv.1 (φyφ)
cbv3hv.2 (ψxψ)
cbv3hv.3 (x = y → (φψ))
Assertion
Ref Expression
cbv3hvOLD (xφyψ)
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   ψ(x,y)

Proof of Theorem cbv3hvOLD
StepHypRef Expression
1 cbv3hv.1 . . 3 (φyφ)
21alimi 1559 . 2 (xφxyφ)
3 ax9v 1655 . . . . 5 ¬ x ¬ x = y
4 hba1 1786 . . . . . . . 8 (xφxxφ)
5 cbv3hv.2 . . . . . . . 8 (ψxψ)
64, 5hbim 1817 . . . . . . 7 ((xφψ) → x(xφψ))
76hbn 1776 . . . . . 6 (¬ (xφψ) → x ¬ (xφψ))
8 sp 1747 . . . . . . . 8 (xφφ)
9 cbv3hv.3 . . . . . . . 8 (x = y → (φψ))
108, 9syl5 28 . . . . . . 7 (x = y → (xφψ))
1110con3i 127 . . . . . 6 (¬ (xφψ) → ¬ x = y)
127, 11alrimih 1565 . . . . 5 (¬ (xφψ) → x ¬ x = y)
133, 12mt3 171 . . . 4 (xφψ)
1413alimi 1559 . . 3 (yxφyψ)
1514a7s 1735 . 2 (xyφyψ)
162, 15syl 15 1 (xφyψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀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-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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