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Theorem hbn1fw 1721
 Description: Weak version of ax-6 1746 from which we can prove any ax-6 1746 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 19-Apr-2017.) (Proof shortened by Wolf Lammen, 28-Feb-2018.)
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 1716 . . . 4
76notbii 289 . . 3
87biimpi 188 . 2
9 hbn1fw.5 . 2
107biimpri 199 . . 3
1110alimi 1569 . 2
128, 9, 113syl 19 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550 This theorem is referenced by:  hbn1w  1723 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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