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Theorem ad2antrl 708

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.)

**Hypothesis**
Ref	Expression
ad2ant.1	⊢ (φ → ψ)

**Assertion**
Ref	Expression
ad2antrl	⊢ ((χ ∧ (φ ∧ θ)) → ψ)

**Proof of Theorem ad2antrl**
Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	adantr 451	. 2 ⊢ ((φ ∧ θ) → ψ)
3	2	adantl 452	1 ⊢ ((χ ∧ (φ ∧ 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: simprl 732 simprll 738 simprlr 739 preaddccan2 4455 ncfinlower 4483 tfinnn 4534 sfinltfin 4535 enadjlem1 6059 sbthlem3 6205 nchoicelem17 6305 nchoice 6308