Theorem ad4ant23 1297

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

Hypothesis

Ref	Expression
ad4ant23.1	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
ad4ant23	|- ( ( ( ( th /\ ph ) /\ ps ) /\ ta ) -> ch )

Proof of Theorem ad4ant23

Step	Hyp	Ref	Expression
1		ad4ant23.1	. . . . 5 |- ( ( ph /\ ps ) -> ch )
2	1	ex 450	. . . 4 |- ( ph -> ( ps -> ch ) )
3	2	a1dd 50	. . 3 |- ( ph -> ( ps -> ( ta -> ch ) ) )
4	3	a1i 11	. 2 |- ( th -> ( ph -> ( ps -> ( ta -> ch ) ) ) )
5	4	imp41 619	1 |- ( ( ( ( th /\ ph ) /\ ps ) /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ wa 384

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

This theorem is referenced by:  fntpb  6473  usgredg2vlem2  26118  umgr3v3e3cycl  27044  matunitlindflem1  33405  matunitlindflem2  33406  heicant  33444  difmap  39399  xlimmnfvlem2  40059  xlimpnfvlem2  40063  sge0resplit  40623  hoidmvle  40814