Theorem biimpac 296

Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)

Hypothesis

Ref	Expression
biimpa.1	⊢ (𝜑 → (𝜓 ↔ 𝜒))

Assertion

Ref	Expression
biimpac	⊢ ((𝜓 ∧ 𝜑) → 𝜒)

Proof of Theorem biimpac

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒))
2	1	biimpcd 158	. 2 ⊢ (𝜓 → (𝜑 → 𝜒))
3	2	imp 123	1 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  gencbvex2  2728  ordtri2or2exmidlem  4436  onsucelsucexmidlem  4439  ordsuc  4473  onsucuni2  4474  poltletr  4934  tz6.12-1  5441  nfunsn  5448  nnaordex  6416  th3qlem1  6524  ssfilem  6762  diffitest  6774  nqnq0pi  7239  distrlem1prl  7383  distrlem1pru  7384  eqle  7848  flodddiv4  11620