Theorem 3an1rs 1163

Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.)

Hypothesis

Ref	Expression
3an1rs.1	⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → τ)

Assertion

Ref	Expression
3an1rs	⊢ (((φ ∧ ψ ∧ θ) ∧ χ) → τ)

Proof of Theorem 3an1rs

Step	Hyp	Ref	Expression
1		3an1rs.1	. . . . . 6 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → τ)
2	1	ex 423	. . . . 5 ⊢ ((φ ∧ ψ ∧ χ) → (θ → τ))
3	2	3exp 1150	. . . 4 ⊢ (φ → (ψ → (χ → (θ → τ))))
4	3	com34 77	. . 3 ⊢ (φ → (ψ → (θ → (χ → τ))))
5	4	3imp 1145	. 2 ⊢ ((φ ∧ ψ ∧ θ) → (χ → τ))
6	5	imp 418	1 ⊢ (((φ ∧ ψ ∧ θ) ∧ χ) → τ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by: (None)