Theorem anabsi5 377

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabsi5.1	⊢ (φ → ((φ ∧ ψ) → χ))

Assertion

Ref	Expression
anabsi5	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsi5

Step	Hyp	Ref	Expression
1		anabsi5.1	. . 3 ⊢ (φ → ((φ ∧ ψ) → χ))
2	1	adantr 306	. 2 ⊢ ((φ ∧ ψ) → ((φ ∧ ψ) → χ))
3	2	pm2.43i 58	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  anabsi6 378  anabsi8 380  rcla4ev 1403  reuuni2 1956  onint 2261  onminex 2275  f1oweOLD 2944  php2 3410  genpprecl 3898  prlem934 3933  axsup 4088  projlem25 5217

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

metamath.org