Theorem ad5antr 496

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 494	. 2 |- ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )
3	2	adantr 276	1 |- ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  ad6antr  498  difinfinf  7300  ctssdclemn0  7309  cauappcvgprlemladdfu  7874  caucvgprlemloc  7895  caucvgprlemladdfu  7897  caucvgprlemlim  7901  caucvgprprlemml  7914  caucvgprprlemloc  7923  caucvgprprlemlim  7931  suplocexprlemmu  7938  suplocexprlemru  7939  suplocexprlemloc  7941  suplocsrlem  8028  axcaucvglemres  8119  nn0ltexp2  10972  resqrexlemglsq  11600  xrmaxifle  11824  xrmaxiflemlub  11826  divalglemeuneg  12502  bezoutlemnewy  12585  4sqlemsdc  12991  ctiunctlemfo  13078  mhmmnd  13721  txmetcnp  15261  mulcncf  15351  suplociccreex  15367  cnplimclemr  15412  limccnpcntop  15418  lgsval  15752