Theorem 3com23 616

Description: Commutation in antecedent. Swap 2nd and 3rd.

Hypothesis

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

Assertion

Ref	Expression
3com23	|- ((ph /\ ch /\ ps) -> th)

Proof of Theorem 3com23

Step	Hyp	Ref	Expression
1		3exp.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3exp 611	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com23 32	. 2 |- (ph -> (ch -> (ps -> th)))
4	3	3imp 608	1 |- ((ph /\ ch /\ ps) -> th)

Syntax hints:   -> wi 2   /\ w3a 581

This theorem is referenced by:  3coml 617  add23t 4126  mul23t 4176  subsubt 4203  ltsub23t 4359  ltsub13t 4360  qbtwnre 4650  hvadd23t 5011  his5 5050  cvntrt 5724  mdsymlem5 5780  sumdmdi 5785

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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