Theorem 3adant2l 856

Description: Deduction adding a conjunct to antecedent.

Hypothesis

Ref	Expression
3adant1l.1	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
3adant2l	|- ((ph /\ (ta /\ ps) /\ ch) -> th)

Proof of Theorem 3adant2l

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3com12 839	. . 3 |- ((ps /\ ph /\ ch) -> th)
3	2	3adant1l 854	. 2 |- (((ta /\ ps) /\ ph /\ ch) -> th)
4	3	3com12 839	1 |- ((ph /\ (ta /\ ps) /\ ch) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 777

This theorem is referenced by:  nvaddsub4 8277

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 779

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