Theorem ad6antr 735

Description: Deduction adding 6 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypothesis

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

Assertion

Ref	Expression
ad6antr	|- ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )

Proof of Theorem ad6antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad5antr 733	. 2 |- ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )
3	2	adantr 465	1 |- ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )

Syntax hints:   -> wi 4   /\ wa 369

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 185  df-an 371

This theorem is referenced by:  ad7antr  737  catass  14622  funcpropd  14808  natpropd  14884  restutop  19810  utopreg  19825  restmetu  20160  tgifscgr  22959  tgcgrxfr  22968  tgbtwnconn1lem3  23004  legtrd  23018  miriso  23071  footex  23107  f1otrge  23116  cusgrares  23378  lgamucov  27022  heicant  28423  mblfinlem3  28427  clwlkisclwwlklem1  30446