Theorem biimpac 282

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 148	. 2 ⊢ (𝜓 → (𝜑 → 𝜒))
3	2	imp 115	1 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  gencbvex2  2601  ordtri2or2exmidlem  4251  onsucelsucexmidlem  4254  ordsuc  4287  onsucuni2  4288  poltletr  4725  tz6.12-1  5200  nfunsn  5207  nnaordex  6100  th3qlem1  6208  ssfiexmid  6336  diffitest  6344  nqnq0pi  6536  distrlem1prl  6680  distrlem1pru  6681  eqle  7109