Theorem 3com13 615

Description: Commutation in antecedent. Swap 1st and 3rd.

Hypothesis

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

Assertion

Ref	Expression
3com13	|- ((ch /\ ps /\ ph) -> th)

Proof of Theorem 3com13

Step	Hyp	Ref	Expression
1		3anrev 590	. 2 |- ((ch /\ ps /\ ph) <-> (ph /\ ps /\ ch))
2		3exp.1	. 2 |- ((ph /\ ps /\ ch) -> th)
3	1, 2	sylbi 174	1 |- ((ch /\ ps /\ ph) -> th)

Syntax hints:   -> wi 2   /\ w3a 581

This theorem is referenced by:  3coml 617  oacan 3150  oaword1 3154  nnmcan 3190  ltapr 3945  ltaddsubt 4357  spansncol 5473  mdsymlem3 5778

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  df-3an 583

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