Theorem 3an1rs 1197

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 114	. . . . 5 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → 𝜏))
3	2	3exp 1180	. . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
4	3	com34 83	. . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏))))
5	4	3imp 1175	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → (𝜒 → 𝜏))
6	5	imp 123	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by: (None)