Theorem syl2ani 358

Description: A syllogism inference.

Hypotheses

Ref	Expression
syl2ani.1	|- (ph -> ((ps /\ ch) -> th))
syl2ani.2	|- (ta -> ps)
syl2ani.3	|- (et -> ch)

Assertion

Ref	Expression
syl2ani	|- (ph -> ((ta /\ et) -> th))

Proof of Theorem syl2ani

Step	Hyp	Ref	Expression
1		syl2ani.1	. . 3 |- (ph -> ((ps /\ ch) -> th))
2		syl2ani.3	. . 3 |- (et -> ch)
3	1, 2	sylan2i 357	. 2 |- (ph -> ((ps /\ et) -> th))
4		syl2ani.2	. 2 |- (ta -> ps)
5	3, 4	sylani 356	1 |- (ph -> ((ta /\ et) -> th))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  sqrle 4765

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

This theorem depends on definitions:  df-bi 128  df-an 198

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