Theorem iba 486

Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121.

Assertion

Ref	Expression
iba	⊢ (φ → (ψ ↔ (ψ ∧ φ)))

Proof of Theorem iba

Step	Hyp	Ref	Expression
1		ancrb 265	. 2 ⊢ ((φ → ψ) ↔ (φ → (ψ ∧ φ)))
2	1	pm5.74ri 445	1 ⊢ (φ → (ψ ↔ (ψ ∧ φ)))

Syntax hints:   → wi 2   ↔ wb 127   ∧ wa 196

This theorem is referenced by:  biantru 543  dedlem0a 567  dedlema 569  unineq 1680  dmsnop 2547  fressnfv 2898  pw2en 3348  ltpiord 3809  ltmpi 3825  mdbr2 5728

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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