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Theorem cbv1h 1633
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-May-2018.)
Hypotheses
Ref Expression
cbv1h.1
cbv1h.2
cbv1h.3
Assertion
Ref Expression
cbv1h

Proof of Theorem cbv1h
StepHypRef Expression
1 nfa1 1434 . 2
2 nfa2 1471 . 2
3 sp 1401 . . . . 5
43sps 1430 . . . 4
5 cbv1h.1 . . . 4
64, 5syl 14 . . 3
72, 6nfd 1416 . 2
8 cbv1h.2 . . . 4
94, 8syl 14 . . 3
101, 9nfd 1416 . 2
11 cbv1h.3 . . 3
124, 11syl 14 . 2
131, 2, 7, 10, 12cbv1 1632 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241 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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  cbv2h  1634
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