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Theorem ax11wlem 1694
Description: Lemma for weak version of ax-11 1715. Uses only Tarski's FOL axiom schemes. In some cases, this lemma may lead to shorter proofs than ax11w 1695. (Contributed by NM, 10-Apr-2017.)
Hypothesis
Ref Expression
ax11wlemw.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
ax11wlem  |-  ( x  =  y  ->  ( ph  ->  A. x ( x  =  y  ->  ph )
) )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem ax11wlem
StepHypRef Expression
1 ax11wlemw.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
2 ax-17 1603 . 2  |-  ( ps 
->  A. x ps )
31, 2ax11i 1628 1  |-  ( x  =  y  ->  ( ph  ->  A. x ( x  =  y  ->  ph )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527
This theorem is referenced by:  ax11w  1695
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603
This theorem depends on definitions:  df-bi 177
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