Theorem 3coml 617

Description: Commutation in antecedent. Rotate left.

Hypothesis

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

Assertion

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

Proof of Theorem 3coml

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3com23 616	. 2 ⊢ ((φ ∧ χ ∧ ψ) → θ)
3	2	3com13 615	1 ⊢ ((ψ ∧ χ ∧ φ) → θ)

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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