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Mirrors > Home > NFE Home > Th. List > ad2antlr | GIF version |
Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.) (Proof shortened by Wolf Lammen, 20-Nov-2012.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (φ → ψ) |
Ref | Expression |
---|---|
ad2antlr | ⊢ (((χ ∧ φ) ∧ θ) → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (φ → ψ) | |
2 | 1 | adantr 451 | . 2 ⊢ ((φ ∧ θ) → ψ) |
3 | 2 | adantll 694 | 1 ⊢ (((χ ∧ φ) ∧ θ) → ψ) |
Colors of variables: wff setvar class |
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: ad3antlr 711 simplr 731 simplrl 736 simplrr 737 ax11eq 2193 ax11el 2194 ltfinirr 4457 sfintfin 4532 caovord3 5631 nntccl 6170 sbthlem3 6205 nchoicelem17 6305 |
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