Theorem ad5ant2345 1317

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

Hypothesis

Ref	Expression
ad5ant2345.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
ad5ant2345	|- ( ( ( ( ( et /\ ph ) /\ ps ) /\ ch ) /\ th ) -> ta )

Proof of Theorem ad5ant2345

Step	Hyp	Ref	Expression
1		ad5ant2345.1	. . . 4 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
2	1	exp41 638	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
3	2	adantl 482	. 2 |- ( ( et /\ ph ) -> ( ps -> ( ch -> ( th -> ta ) ) ) )
4	3	imp41 619	1 |- ( ( ( ( ( et /\ ph ) /\ ps ) /\ ch ) /\ th ) -> ta )

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:  mblfinlem2  33447  liminflelimsuplem  40007  climxlim2lem  40071  iundjiun  40677