Theorem ad5ant245 1307

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)

Hypothesis

Ref	Expression
ad5ant245.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
ad5ant245	|- ( ( ( ( ( ta /\ ph ) /\ et ) /\ ps ) /\ ch ) -> th )

Proof of Theorem ad5ant245

Step	Hyp	Ref	Expression
1		ad5ant245.1	. . . . 5 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3exp 1264	. . . 4 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	a1i13 27	. . 3 |- ( ta -> ( ph -> ( et -> ( ps -> ( ch -> th ) ) ) ) )
4	3	imp 445	. 2 |- ( ( ta /\ ph ) -> ( et -> ( ps -> ( ch -> th ) ) ) )
5	4	imp41 619	1 |- ( ( ( ( ( ta /\ ph ) /\ et ) /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ 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:  2pthnloop  26627  matunitlindflem1  33405  nnfoctbdjlem  40672  sfprmdvdsmersenne  41520