Theorem anabsi7 379

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabsi7.1	⊢ (ψ → ((φ ∧ ψ) → χ))

Assertion

Ref	Expression
anabsi7	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsi7

Step	Hyp	Ref	Expression
1		anabsi7.1	. . . 4 ⊢ (ψ → ((φ ∧ ψ) → χ))
2	1	exp3a 292	. . 3 ⊢ (ψ → (φ → (ψ → χ)))
3	2	pm2.43b 61	. 2 ⊢ (φ → (ψ → χ))
4	3	imp 277	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  anabss7 385  elunii 1924  ordelord 2221  vtoclibr 2451  opelxpi 2455  fneu 2728  fvelrn 2883  fvrn 2888  sdomtr 3373  prnmax 3893

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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