Theorem 3coml 617

Description: Commutation in antecedent. Rotate left.

Hypothesis

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

Assertion

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

Proof of Theorem 3coml

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ((ph /\ ps /\ ch) -> th)
2	1	3com23 616	. 2 |- ((ph /\ ch /\ ps) -> th)
3	2	3com13 615	1 |- ((ps /\ ch /\ ph) -> th)

Syntax hints:   -> wi 2   /\ w3a 581

This theorem is referenced by:  3comr 618  oaword 3151  ltapq 3870  ltmpq 3871  ltasr 4003  adddirt 4103  addcan2t 4123  ltaddsubt 4357  qbtwnre 4650

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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