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Theorem ralxfrALT 4199
 Description: Transfer universal quantification from a variable to another variable contained in expression . This proof does not use ralxfrd 4194. (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 2652 . . . . 5
41, 3syl 14 . . . 4
54com12 27 . . 3
65ralrimiv 2391 . 2
7 ralxfr.2 . . . 4
8 nfra1 2355 . . . . 5
9 nfv 1421 . . . . 5
10 rsp 2369 . . . . . 6
112biimprcd 149 . . . . . 6
1210, 11syl6 29 . . . . 5
138, 9, 12rexlimd 2430 . . . 4
147, 13syl5 28 . . 3
1514ralrimiv 2391 . 2
166, 15impbii 117 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  wral 2306  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559 This theorem is referenced by: (None)
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