Theorem 3com12 614

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

Hypothesis

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

Assertion

Ref	Expression
3com12	⊢ ((ψ ∧ φ ∧ χ) → θ)

Proof of Theorem 3com12

Step	Hyp	Ref	Expression
1		3exp.1	. . . 4 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3exp 611	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	com12 13	. 2 ⊢ (ψ → (φ → (χ → θ)))
4	3	3imp 608	1 ⊢ ((ψ ∧ φ ∧ χ) → θ)

Syntax hints:   → wi 2   ∧ w3a 581

This theorem is referenced by:  nnmord 3189  ecopoprtrn 3247  add12t 4125  addsubt 4151  div23t 4240  ltaddsub2t 4358  ledivt 4405  ltmuldiv2t 4407  hvadd12t 5012  his5 5050

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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