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  7936  mulnqpru  7937  distrlem5prl  7954  distrlem5pru  7955  recexprlemss1l  8003  recexprlemss1u  8004  lemul12a  9195  nnmulcl  9328  elfz0fzfz0  10544  fzo1fzo0n0  10606  fzofzim  10611  elincfzoext  10622  elfzodifsumelfzo  10630  le2sq2  11066  swrdswrd  11492  swrdccat3blem  11526  oddprmgt2  12931  infpnlem1  13160  lmodvsdi  14699