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Theorem dvelimhw 1849
 Description: Proof of dvelimh 1964 without using ax-12 1925 but with additional distinct variable conditions. (Contributed by Andrew Salmon, 21-Jul-2011.) (Revised by NM, 1-Aug-2017.)
Hypotheses
Ref Expression
dvelimhw.1
dvelimhw.2
dvelimhw.3
dvelimhw.4
Assertion
Ref Expression
dvelimhw
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem dvelimhw
StepHypRef Expression
1 ax-17 1616 . . 3
2 hbn1 1730 . . . 4
3 equcomi 1679 . . . . 5
4 dvelimhw.4 . . . . 5
5 equcomi 1679 . . . . . 6
65alimi 1559 . . . . 5
73, 4, 6syl56 30 . . . 4
8 dvelimhw.1 . . . . 5
98a1i 10 . . . 4
102, 7, 9hbimd 1815 . . 3
111, 10hbald 1740 . 2
12 dvelimhw.2 . . 3
13 dvelimhw.3 . . 3
1412, 13equsalhw 1838 . 2
1514albii 1566 . 2
1611, 14, 153imtr3g 260 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax12olem6  1932
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