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Theorem ex3 31167
Description: Apply ex 434 to a hypothesis with a 3-right-nested conjunction antecedent, with the antecedent of the assertion being a triple conjunction rather than a 2-right-nested conjunction. (Contributed by Alan Sare, 22-Apr-2018.)
Hypothesis
Ref Expression
ex3.1  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
ex3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )

Proof of Theorem ex3
StepHypRef Expression
1 df-3an 967 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
2 ex3.1 . . 3  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
32ex 434 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( th  ->  ta ) )
41, 3sylbi 195 1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967
This theorem is referenced by:  iunconlem2  31558
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