Theorem ad2antll 709

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

Hypothesis

Ref	Expression
ad2ant.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ad2antll	⊢ ((χ ∧ (θ ∧ φ)) → ψ)

Proof of Theorem ad2antll

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	adantl 452	. 2 ⊢ ((θ ∧ φ) → ψ)
3	2	adantl 452	1 ⊢ ((χ ∧ (θ ∧ φ)) → ψ)

Syntax hints:   → wi 4   ∧ wa 358

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

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

This theorem is referenced by:  simprr  733  simprrl  740  simprrr  741  ax11eq  2193  ax11el  2194  tfinsuc  4499  sfinltfin  4536  vfinspsslem1  4551  vfinspclt  4553  enadjlem1  6060