Theorem exp4b 367

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Nov-2012.)

Hypothesis

Ref	Expression
exp4b.1	⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → 𝜏))

Assertion

Ref	Expression
exp4b	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp4b

Step	Hyp	Ref	Expression
1		exp4b.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → 𝜏))
2	1	ex 115	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
3	2	exp4a 366	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exp43  372  reuss2  3487  nndi  6654  mulnqprl  7788  mulnqpru  7789  distrlem5prl  7806  distrlem5pru  7807  recexprlemss1l  7855  recexprlemss1u  7856  lemul12a  9042  nnmulcl  9164  elfz0fzfz0  10361  fzo1fzo0n0  10423  fzofzim  10428  elincfzoext  10439  elfzodifsumelfzo  10447  le2sq2  10878  swrdswrd  11290  swrdccat3blem  11324  oddprmgt2  12711  infpnlem1  12937  lmodvsdi  14331