Theorem exp32 363

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp32.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)

Assertion

Ref	Expression
exp32	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Proof of Theorem exp32

Step	Hyp	Ref	Expression
1		exp32.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
2	1	ex 114	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
3	2	expd 256	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by:  exp44  371  exp45  372  expr  373  anassrs  398  an13s  557  3impb  1181  xordidc  1381  f0rn0  5363  funfvima3  5697  isoini  5765  ovg  5956  fundmen  6748  distrlem1prl  7497  distrlem1pru  7498  caucvgprprlemaddq  7623  recexgt0sr  7688  axpre-suploclemres  7816  cnegexlem2  8046  mulgt1  8729  faclbnd  10610  divgcdcoprm0  11972  cncongr2  11975  oddpwdclemdvds  12039  oddpwdclemndvds  12040  cnpnei  12606