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))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  exp43  372  reuss2  3513  nndi  6759  mulnqprl  7935  mulnqpru  7936  distrlem5prl  7953  distrlem5pru  7954  recexprlemss1l  8002  recexprlemss1u  8003  lemul12a  9193  nnmulcl  9326  elfz0fzfz0  10535  fzo1fzo0n0  10597  fzofzim  10602  elincfzoext  10613  elfzodifsumelfzo  10621  le2sq2  11054  swrdswrd  11479  swrdccat3blem  11513  oddprmgt2  12914  infpnlem1  13140  lmodvsdi  14650