Theorem ad5antr 479

Description: Deduction adding 5 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypothesis

Ref	Expression
ad2ant.1	|- ( ph -> ps )

Assertion

Ref	Expression
ad5antr	|- ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Proof of Theorem ad5antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad4antr 477	. 2 |- ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )
3	2	adantr 270	1 |- ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  ad6antr  481  cauappcvgprlemladdfu  6844  caucvgprlemloc  6865  caucvgprlemladdfu  6867  caucvgprlemlim  6871  caucvgprprlemml  6884  caucvgprprlemloc  6893  caucvgprprlemlim  6901  axcaucvglemres  7065  resqrexlemglsq  9908  divalglemeuneg  10323  bezoutlemnewy  10385