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  3485  nndi  6649  mulnqprl  7781  mulnqpru  7782  distrlem5prl  7799  distrlem5pru  7800  recexprlemss1l  7848  recexprlemss1u  7849  lemul12a  9035  nnmulcl  9157  elfz0fzfz0  10354  fzo1fzo0n0  10415  fzofzim  10420  elincfzoext  10431  elfzodifsumelfzo  10439  le2sq2  10870  swrdswrd  11279  swrdccat3blem  11313  oddprmgt2  12699  infpnlem1  12925  lmodvsdi  14318