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Theorem ralxfrALT 4771
 Description: Transfer universal quantification from a variable to another variable contained in expression . This proof does not use ralxfrd 4766. (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 3054 . . . . 5
41, 3syl 16 . . . 4
54com12 30 . . 3
65ralrimiv 2794 . 2
7 ralxfr.2 . . . 4
8 nfra1 2762 . . . . 5
9 nfv 1630 . . . . 5
10 rsp 2772 . . . . . 6
112biimprcd 218 . . . . . 6
1210, 11syl6 32 . . . . 5
138, 9, 12rexlimd 2833 . . . 4
147, 13syl5 31 . . 3
1514ralrimiv 2794 . 2
166, 15impbii 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653   wcel 1727  wral 2711  wrex 2712 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-v 2964
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