Theorem ex3 1190

Description: Apply ex 114 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

Step	Hyp	Ref	Expression
1		ex3.1	. . 3 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
2	1	ex 114	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> ( th -> ta ) )
3	2	3impa 1189	1 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by: (None)