Theorem ad4antr 463

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

Hypothesis

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

Assertion

Ref	Expression
ad4antr	|- ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )

Proof of Theorem ad4antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad3antrrr 461	. 2 |- ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) -> ps )
3	2	adantr 261	1 |- ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem is referenced by:  ad5antr  465  cauappcvgprlemloc  6750  caucvgprlemm  6766  caucvgprlemladdrl  6776  caucvgprlemlim  6779  caucvgprprlemml  6792  caucvgprprlemexbt  6804  caucvgprprlemlim  6809  caucvgsrlemgt1  6879  axcaucvglemres  6973  rebtwn2zlemstep  9107  caucvgre  9580  cvg1nlemres  9584  resqrexlemglsq  9620