Theorem sylan2d 353

Description: A syllogism deduction.

Hypotheses

Ref	Expression
sylan2d.1	|- (ph -> ((ps /\ ch) -> th))
sylan2d.2	|- (ph -> (ta -> ch))

Assertion

Ref	Expression
sylan2d	|- (ph -> ((ps /\ ta ) -> th))

Proof of Theorem sylan2d

Step	Hyp	Ref	Expression
1		sylan2d.1	. . . 4 |- (ph -> ((ps /\ ch) -> th))
2	1	ancomsd 335	. . 3 |- (ph -> ((ch /\ ps) -> th))
3		sylan2d.2	. . 3 |- (ph -> (ta -> ch))
4	2, 3	syland 352	. 2 |- (ph -> ((ta /\ ps) -> th))
5	4	ancomsd 335	1 |- (ph -> ((ps /\ ta ) -> th))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  syl2and 354  sylan2i 357  unblem1 3431  unfi 3441

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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