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Mirrors > Home > NFE Home > Th. List > simplrr | GIF version |
Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.) |
Ref | Expression |
---|---|
simplrr | ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 447 | . 2 ⊢ ((ψ ∧ χ) → χ) | |
2 | 1 | ad2antlr 707 | 1 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → χ) |
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 tfinnn 4534 enprmaplem3 6078 ncdisjun 6136 |
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