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Theorem a1i4 25613
Description: Add an antecedent to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.)
Hypothesis
Ref Expression
a1i4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Assertion
Ref Expression
a1i4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem a1i4
StepHypRef Expression
1 a1i4.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
2 ax-1 5 . 2  |-  ( ta 
->  ( th  ->  ta ) )
31, 2syl8 65 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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