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Theorem ax4wK 28153
 Description: Weak version of ax-4 1692. Uses only Tarski's FOL axiom schemes (see description for equidK 28136). Lemma 9 of [KalishMontague] p. 86. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
ax4wK.1
Assertion
Ref Expression
ax4wK
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ax4wK
StepHypRef Expression
1 ax4wK.1 . . . . 5
21biimpd 200 . . . 4
32a4imvK 28151 . . 3
43ax-gen 1536 . 2
5 ax-5 1533 . . 3
6 ax-17 1628 . . . 4
7 equcomiK 28137 . . . . . 6
81biimprd 216 . . . . . 6
97, 8syl 17 . . . . 5
109a4imvK 28151 . . . 4
116, 10imim12i 55 . . 3
125, 11syl 17 . 2
134, 12ax-mp 10 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532 This theorem is referenced by:  ax4vK  28154  ax4falK  28157  hba1wK  28167  ax11wK  28174  ax12o10lem7K  28193 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9v 1632 This theorem depends on definitions:  df-bi 179
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