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Theorem hbequid 1494
 Description: Bound-variable hypothesis builder for . This theorem tells us that any variable, including , is effectively not free in , even though is technically free according to the traditional definition of free variable. (The proof uses only ax-5 1424, ax-8 1483, ax-12 1490, and ax-gen 1426. This shows that this can be proved without ax-9 1512, even though the theorem equid 1678 cannot be. A shorter proof using ax-9 1512 is obtainable from equid 1678 and hbth 1440.) (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 23-Mar-2014.)
Assertion
Ref Expression
hbequid

Proof of Theorem hbequid
StepHypRef Expression
1 ax12or 1491 . 2
2 ax-8 1483 . . . . . 6
32pm2.43i 49 . . . . 5
43alimi 1432 . . . 4
54a1d 22 . . 3
6 ax-4 1488 . . . 4
75, 6jaoi 706 . . 3
85, 7jaoi 706 . 2
91, 8ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 698  wal 1330   wceq 1332 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-gen 1426  ax-8 1483  ax-i12 1486  ax-4 1488 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  equveli  1733
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