Theorem 3ad2antr3 1159

Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 30-Dec-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antr3	|- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )

Proof of Theorem 3ad2antr3

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantrl 475	. 2 |- ( ( ph /\ ( ta /\ ch ) ) -> th )
3	2	3adantr1 1151	1 |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

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 depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  ordwe  4560  grprcan  12740