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  3505  nndi  6732  mulnqprl  7899  mulnqpru  7900  distrlem5prl  7917  distrlem5pru  7918  recexprlemss1l  7966  recexprlemss1u  7967  lemul12a  9153  nnmulcl  9275  elfz0fzfz0  10482  fzo1fzo0n0  10544  fzofzim  10549  elincfzoext  10560  elfzodifsumelfzo  10568  le2sq2  11001  swrdswrd  11422  swrdccat3blem  11456  oddprmgt2  12856  infpnlem1  13082  lmodvsdi  14571