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Theorem wl-syls2 31857
Description: Replacing a nested antecedent. A sort of syllogism in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
wl-syls2.1  |-  ( ph  ->  ps )
wl-syls2.2  |-  ( (
ph  ->  ch )  ->  th )
Assertion
Ref Expression
wl-syls2  |-  ( ( ps  ->  ch )  ->  th )

Proof of Theorem wl-syls2
StepHypRef Expression
1 wl-syls2.1 . . 3  |-  ( ph  ->  ps )
21imim1i 60 . 2  |-  ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )
3 wl-syls2.2 . 2  |-  ( (
ph  ->  ch )  ->  th )
42, 3syl 17 1  |-  ( ( ps  ->  ch )  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by: (None)
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