Theorem ad7antr 497

Description: Deduction adding 7 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypothesis

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

Assertion

Ref	Expression
ad7antr	|- ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps )

Proof of Theorem ad7antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad6antr 495	. 2 |- ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )
3	2	adantr 274	1 |- ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> 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:  ad8antr  499