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Theorem simplrl 736

Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.)

**Assertion**
Ref	Expression
simplrl	⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → ψ)

**Proof of Theorem simplrl**
Step	Hyp	Ref	Expression
1		simpl 443	. 2 ⊢ ((ψ ∧ χ) → ψ)
2	1	ad2antlr 707	1 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → ψ)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360

This theorem is referenced by: pm2.61da3ne 2596 rmob 3134 preaddccan2 4455 ncfinraise 4481 tfindi 4496 evenodddisj 4516 sfintfin 4532 ncdisjun 6136