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Theorem dvelimfALT2OLD 29177
 Description: Proof of dvelimh 1969 using dveeq2 1945 (shown as the last hypothesis) instead of ax12o 1939. As a consequence, theorem a12study2 29186 shows that ax12o 1939 could be replaced by dveeq2 1945 (the last hypothesis). (Contributed by Andrew Salmon, 21-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) Obsolete as of 1-Aug-2017 - NM.
Hypotheses
Ref Expression
dvelimfALT2OLD.1
dvelimfALT2OLD.2
dvelimfALT2OLD.3
dvelimfALT2OLD.4
Assertion
Ref Expression
dvelimfALT2OLD
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem dvelimfALT2OLD
StepHypRef Expression
1 ax-17 1616 . . 3
2 hbn1 1730 . . . 4
3 dvelimfALT2OLD.4 . . . 4
4 dvelimfALT2OLD.1 . . . . 5
54a1i 10 . . . 4
62, 3, 5hbimd 1817 . . 3
71, 6hbald 1740 . 2
8 dvelimfALT2OLD.2 . . 3
9 dvelimfALT2OLD.3 . . 3
108, 9equsalh 1966 . 2
1110albii 1566 . 2
127, 10, 113imtr3g 260 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176  wal 1540   wceq 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
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