axmp - Higher-Order Logic Explorer

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Theorem axmp 193

Description: Rule of Modus Ponens. The postulated inference rule of propositional calculus. See e.g. Rule 1 of [Hamilton] p. 73.

**Assertion**
Ref	Expression
axmp	⊢ ⊤⊧S

**Proof of Theorem axmp**
Step	Hyp	Ref	Expression
1		axmp.1	. 2 ⊢ S:∗
2		axmp.2	. 2 ⊢ ⊤⊧R
3		axmp.3	. 2 ⊢ ⊤⊧[R ⇒ S]
4	1, 2, 3	mpd 146	1 ⊢ ⊤⊧S

Colors of variables: type var term

Syntax hints: ∗hb 3 ⊤kt 8 [kbr 9 ⊧wffMMJ2 11 wffMMJ2t 12 ⇒ tim 111

This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103

This theorem depends on definitions: df-ov 65 df-an 118 df-im 119

This theorem is referenced by: (None)