Theorem syl3anr2 875

Description: A syllogism inference.

Hypotheses

Ref	Expression
syl3anr1.1	|- ((ph /\ (ps /\ ch /\ th)) -> ta)
syl3anr2.2	|- (et -> ch)

Assertion

Ref	Expression
syl3anr2	|- ((ph /\ (ps /\ et /\ th)) -> ta)

Proof of Theorem syl3anr2

Step	Hyp	Ref	Expression
1		syl3anr1.1	. . . 4 |- ((ph /\ (ps /\ ch /\ th)) -> ta)
2	1	ancoms 436	. . 3 |- (((ps /\ ch /\ th) /\ ph) -> ta)
3		syl3anr2.2	. . 3 |- (et -> ch)
4	2, 3	syl3anl2 871	. 2 |- (((ps /\ et /\ th) /\ ph) -> ta)
5	4	ancoms 436	1 |- ((ph /\ (ps /\ et /\ th)) -> ta)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 773

This theorem is referenced by:  vcsubdir 8112  ipassr2 8438

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 775

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