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Theorem ralxfrALT 4610
 Description: Alternate proof of ralxfr 4609 which does not use ralxfrd 4605. (Contributed by NM, 10-Jun-2005.) (Revised by Mario Carneiro, 15-Aug-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ralxfr.1
ralxfr.2
ralxfr.3
Assertion
Ref Expression
ralxfrALT
Distinct variable groups:   ,   ,   ,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem ralxfrALT
StepHypRef Expression
1 ralxfr.1 . . . . 5
2 ralxfr.3 . . . . . 6
32rspcv 3156 . . . . 5
41, 3syl 17 . . . 4
54com12 29 . . 3
65ralrimiv 2816 . 2
7 ralxfr.2 . . . 4
8 nfra1 2785 . . . . 5
9 nfv 1728 . . . . 5
10 rsp 2770 . . . . . 6
112biimprcd 225 . . . . . 6
1210, 11syl6 31 . . . . 5
138, 9, 12rexlimd 2888 . . . 4
147, 13syl5 30 . . 3
1514ralrimiv 2816 . 2
166, 15impbii 187 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1405   wcel 1842  wral 2754  wrex 2755 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-rex 2760  df-v 3061 This theorem is referenced by: (None)
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