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  3489  nndi  6697  mulnqprl  7831  mulnqpru  7832  distrlem5prl  7849  distrlem5pru  7850  recexprlemss1l  7898  recexprlemss1u  7899  lemul12a  9085  nnmulcl  9207  elfz0fzfz0  10404  fzo1fzo0n0  10466  fzofzim  10471  elincfzoext  10482  elfzodifsumelfzo  10490  le2sq2  10921  swrdswrd  11333  swrdccat3blem  11367  oddprmgt2  12767  infpnlem1  12993  lmodvsdi  14387