Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax7wK Unicode version

Theorem ax7wK 27819
 Description: Weak version of ax-7 1535 from which we can prove any ax-7 1535 instance not involving wff variables or bundling. Uses only Tarski's predicate calculus axiom schemes i.e. does not use ax-6 1534, ax-7 1535, ax-11 1624, or ax-12 1633, and uses ax-9v 1632 instead of ax-9 1684. Unlike ax-7 1535, this theorem requires that and be distinct i.e. are not bundled. See the description in the comment of equidK 27792. (Contributed by NM, 10-Apr-2017.)
Hypothesis
Ref Expression
ax7wK.1
Assertion
Ref Expression
ax7wK
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem ax7wK
StepHypRef Expression
1 ax7wK.1 . . . . 5
21biimpd 200 . . . 4
32cbvalivK 27811 . . 3
43alimiK 27798 . 2
5 ax-17 1628 . 2
6 equcomiK 27793 . . . . . 6
71biimprd 216 . . . . . 6
86, 7syl 17 . . . . 5
98a4imvK 27805 . . . 4
109alimiK 27798 . . 3
1110alimiK 27798 . 2
124, 5, 113syl 20 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532   wceq 1619 This theorem is referenced by:  hbalwK  27820 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
 Copyright terms: Public domain W3C validator