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Theorem hbn1fw 1705
 Description: Weak version of ax-6 1729 from which we can prove any ax-6 1729 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 19-Apr-2017.)
Hypotheses
Ref Expression
hbn1fw.1
hbn1fw.2
hbn1fw.3
hbn1fw.4
hbn1fw.5
hbn1fw.6
Assertion
Ref Expression
hbn1fw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem hbn1fw
StepHypRef Expression
1 hbn1fw.1 . . . . 5
2 hbn1fw.2 . . . . 5
3 hbn1fw.3 . . . . 5
4 hbn1fw.4 . . . . 5
5 hbn1fw.6 . . . . 5
61, 2, 3, 4, 5cbvalw 1701 . . . 4
76biimpri 197 . . 3
87con3i 127 . 2
9 hbn1fw.5 . 2
106biimpi 186 . . . 4
1110con3i 127 . . 3
1211alimi 1559 . 2
138, 9, 123syl 18 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  hbn1w  1706
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