Theorem 3adantr2 809

Description: Deduction adding a conjunct to antecedent.

Hypothesis

Ref	Expression
3adantr.1	⊢ ((φ ⋀ (ψ ⋀ χ)) → θ)

Assertion

Ref	Expression
3adantr2	⊢ ((φ ⋀ (ψ ⋀ τ ⋀ χ)) → θ)

Proof of Theorem 3adantr2

Step	Hyp	Ref	Expression
1		3adantr.1	. . . 4 ⊢ ((φ ⋀ (ψ ⋀ χ)) → θ)
2	1	ancoms 438	. . 3 ⊢ (((ψ ⋀ χ) ⋀ φ) → θ)
3	2	3adantl2 806	. 2 ⊢ (((ψ ⋀ τ ⋀ χ) ⋀ φ) → θ)
4	3	ancoms 438	1 ⊢ ((φ ⋀ (ψ ⋀ τ ⋀ χ)) → θ)

Syntax hints:   → wi 3   ⋀ wa 223   ⋀ w3a 777

This theorem is referenced by:  3adant3r2 845  po3nr 2854  bl2in 7840  tgioolem 7911  nvmdi 8266  mdsl3t 10238

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 779

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