Theorem ad6antr 489

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 487	. 2 |- ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )
3	2	adantr 274	1 |- ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  ad7antr  491  supinfneg  9383  infsupneg  9384  cvg1nlemres  10750  suplociccreex  12760