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Theorem frege58bcor 36570
Description: Lemma for frege59b 36571. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege58bcor  |-  ( A. x ( ph  ->  ps )  ->  ( [
y  /  x ] ph  ->  [ y  /  x ] ps ) )

Proof of Theorem frege58bcor
StepHypRef Expression
1 ax-frege58b 36568 . 2  |-  ( A. x ( ph  ->  ps )  ->  [ y  /  x ] ( ph  ->  ps ) )
2 sbim 2244 . 2  |-  ( [ y  /  x ]
( ph  ->  ps )  <->  ( [ y  /  x ] ph  ->  [ y  /  x ] ps )
)
31, 2sylib 201 1  |-  ( A. x ( ph  ->  ps )  ->  ( [
y  /  x ] ph  ->  [ y  /  x ] ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450   [wsb 1805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104  ax-frege58b 36568
This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806
This theorem is referenced by:  frege59b  36571  frege62b  36574
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