Theorem 4animp1 38703

Description: A single hypothesis unification deduction with an assertion which is an implication with a 4-right-nested conjunction antecedent. (Contributed by Alan Sare, 30-May-2018.)

Hypothesis

Ref	Expression
4animp1.1	|- ( ( ph /\ ps /\ ch ) -> ( ta <-> th ) )

Assertion

Ref	Expression
4animp1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Proof of Theorem 4animp1

Step	Hyp	Ref	Expression
1		simpr 477	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> th )
2		4animp1.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> ( ta <-> th ) )
3	2	ad4ant123 1294	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ( ta <-> th ) )
4	1, 3	mpbird 247	1 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  sineq0ALT  39173