Theorem 3com23 616

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

Hypothesis

Ref	Expression
3exp.1	⊢ ((φ ∧ ψ ∧ χ) → θ)

Assertion

Ref	Expression
3com23	⊢ ((φ ∧ χ ∧ ψ) → θ)

Proof of Theorem 3com23

Step	Hyp	Ref	Expression
1		3exp.1	. . . 4 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3exp 611	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	com23 32	. 2 ⊢ (φ → (χ → (ψ → θ)))
4	3	3imp 608	1 ⊢ ((φ ∧ χ ∧ ψ) → θ)

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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